The word for Holiness in Greek is agiothtoV it is translated as holiness or sanctification, these terms are interchangeable. It means to separate or set apart to God from profane things. The word is from agiaV meaning a holy thing or a saint. Most people get mixed up about holiness and righteousness. Righteousness doing good. Holiness is a state being dedicated to the LORD. All Christians who want to serve God are already holy, but may not be very righteous. Holiness and righteousness should go hand in hand, however.

In Colossians 3:5,10 Paul talks about putting off the old man and putting on the new man. This means we are to sanctify or separate ourselves to the LORD with righteousness and to crucify or separate ourselves from sin. Look at how the words are used in scripture:

Sanctified
Romans 15:16 to be a minister of Christ Jesus to the Gentiles in the priestly service of the gospel of God, so that the offering of the Gentiles may be acceptable, sanctified by the Holy Spirit.
Ephesians 5:26 in order to make her holy by cleansing her with the washing of water by the word,
1 Thessalonians 5:23 May the God of peace himself sanctify you entirely; and may your spirit and soul and body be kept sound and blameless at the coming of our Lord Jesus Christ.
Hebrews 10:14 For by a single offering he has perfected for all time those who are sanctified.
1 Timothy 4:5 for it is sanctified by God's word and by prayer.
1 Peter 3:15 but in your hearts sanctify Christ as Lord (NRSV)

Crucified
Romans 6:6 ... our old self was crucified with him so that the body of sin might be destroyed, and we might no longer be enslaved to sin.
Galatians 2:19 For through the law I died to the law, so that I might live to God. I have been crucified with Christ;
Galatians 6:14...Lord Jesus Christ, by which the world has been crucified to me, and I to the world.
Galatians 5:24 And those who belong to Christ Jesus have crucified the flesh with its passions and desires. (NRSV)

Romans 6:19-22 I am speaking in human terms because of your natural limitations. For just as you once presented your members as slaves to impurity and to greater and greater iniquity, so now present your members as slaves to righteousness for sanctification. ²⁰ When you were slaves of sin, you were free in regard to righteousness. ²² But now that you have been freed from sin and enslaved to God, the advantage you get is sanctification. The end is eternal life. (NRSV)

The more you sin the more wicked you become and the less good you do. The more you practice doing good the better you become at it and you begin to sin less. This is called progressive sanctification.
Galatians 5:24-25 And those who belong to Christ Jesus have crucified the flesh with its passions and desires. ²⁵ If we live by the Spirit, let us also be guided by the Spirit. (NRSV)
If Christians allow themselves to be guided by the Holy Spirit and set their minds on righteousness and not on sin they will be walking in the spirit.

Walking in the Spirit
Romans 7:22-8:8 For I delight in the law of God in my inmost self, ²³ but I see in my members another law at war with the law of my mind, making me captive to the law of sin that dwells in my members. ²⁴ Wretched man that I am! Who will rescue me from this body of death? ²⁵ Thanks be to God through Jesus Christ our Lord! So then, with my mind I am a slave to the law of God, but with my flesh I am a slave to the law of sin. 8:1 There is therefore now no condemnation for those who are in Christ Jesus. ² For the law of the Spirit of life in Christ Jesus has set you free from the law of sin and of death. ³ For God has done what the law, weakened by the flesh, could not do: by sending his own Son in the likeness of sinful flesh, and to deal with sin, he condemned sin in the flesh, ⁴ so that the just requirement of the law might be fulfilled in us, who walk not according to the flesh but according to the Spirit. ⁵ For those who live according to the flesh set their minds on the things of the flesh, but those who live according to the Spirit set their minds on the things of the Spirit. ⁶ To set the mind on the flesh is death, but to set the mind on the Spirit is life and peace. ⁷ For this reason the mind that is set on the flesh is hostile to God; it does not submit to God's law -- indeed it cannot, (NRSV)

law of God : "You shall love your neighbor as yourself."
law of faith : trusting in Jesus to save you apart from the works of the law of Moses.
law of works : trying to be saved and stay saved by keeping the law of Moses. Romans 9:31-32
Law of my mind : with his mind he really wants to do righteousness and not sin.
law of the spirit : Christ paid for your sins and will gave you eternal life, if you ask.
law of sin : we have sin nature which makes us sin and always produces death.
Walking in the spirit : concentrating on righteousness or doing good for God and others.
Walking in the flesh : concentrating on sin or even worrying about how not to sin.

True holiness is focusing on doing the work of God and this brings peace. False holiness is focusing on how not to sin, which Paul says brings no peace of mind only death. False holiness is one type of dead work.

Dead works
Hebrews 9:14 How much more shall the blood of Christ, who through the eternal Spirit offered himself without spot to God, purge your conscience from dead works to serve the living God? (KJV)

Jesus blood cleanses you from sin only when you truly believe and repent, likewise the Holy Spirit can purge you of Dead Works only when you understand what they are. Your conscience must be purged of them in order to serve completely God in truth.

Hebrews 6:1 Therefore leaving the principles of the doctrine of Christ, let us go on unto perfection; not laying again the foundation of repentance from dead works, and of faith toward God, (KJV)

The first step you must take in order to grow into being a mature Christian is repentance from Dead Works and secondarily start walking in Faith.
A dead work would be Sinning, worrying how not to sin, or even doing something good, instead of what God would have you to do. When the LORD is not having you do something important for him, you can do good things for yourself and others. It is a question of priorities.
Once you have determined what your dead works are then you can start walking in faith. When you know your doing God’s will for your life you can relax and have fun serving God.

Matthew 21:28-32 "What do you think? A man had two sons; he went to the first and said, ‘Son, go and work in the vineyard today.’ ²⁹ He answered, ‘I will not’; but later he changed his mind and went. ³⁰ The father went to the second and said the same; and he answered, ‘I go, sir’; but he did not go. ³¹ Which of the two did the will of his father?" They said, "The first." Jesus said to them, "Truly I tell you, the tax collectors and the prostitutes are going into the kingdom of God ahead of you. ³² For John came to you in the way of righteousness and you did not believe him, but the tax collectors and the prostitutes believed him; and even after you saw it, you did not change your minds and believe him. (NRSV)

What would you rather have for your child, a pure hart and doing a lot for the LORD but occasionally falling into sin OR a perfect person never sinning in the least and never doing anything for the LORD.

Your children or bible students will learn everything about the world, the only question is, "do you also want them to learn the ways of God?" It is a trick of Satan to have us spend our time on the evil and sin in the world instead of focusing on what God would have us do. The more time you spend guarding against worldly things the less time you will have to teach them of the bible, and the way of life God would have for them.

When Jeremiah, 10:2, said "Learn not the way of the heathen" He means not to learn to practice those ways, not to be ignorant of them. Paul said, in 2 Corinthians 2:11, not be outwitted by Satan by being ignorant of his ways. Jesus said, in John 17:15, "My prayer is not that you take them out of the world but that you protect them from the evil one." (NIV) Jesus also said to be wise as serpents but as gentile as doves. If we are ignorant how can we help?

Luke 10:38-42 Now as they went on their way, he entered a certain village, where a woman named Martha welcomed him into her home. ³⁹ She had a sister named Mary, who sat at the Lord’s feet and listened to what he was saying. ⁴⁰ But Martha was distracted by her many tasks; so she came to him and asked, "Lord, do you not care that my sister has left me to do all the work by myself? Tell her then to help me." ⁴¹ But the Lord answered her, "Martha, Martha, you are worried and distracted by many things; ⁴² there is need of only one thing. Mary has chosen the better part, which will not be taken away from her." (NRSV)

It is another trick of Satan to get us so busy with "things," even righteous acts that help a lot of people, that we do not have time for God.
The following traditions are how Satan makes void the word of God (Mat. 15:3)

Hyper-Armenian
The belief that every time you do the slightest thing wrong you loose your salvation. Resulting in worrying and wasting time you could be spending working for the kingdom. The belief that God doesn’t know the future.

Hyper-Calvinist
The belief that since it is impossible to lose your salvation I’ll go out and sin because I can get away with it. Resulting in a life wrecked by sin. The belief that God forces everything to come out as he wills, including sin.

Hyper-Faith
Faith is a force therefore, I’ll command things to be done. Resulting in death and the loss of many blessings that God has for us.

Hyper-Grace
Grace is a power therefore, I’ll use this power to become perfect. Resulting in self-righteous pride.

Hyper-Charismatic
If you don’t speak in tongues you don’t have the Holy Spirit. Some even go so far to say that means you are not saved.

Anti-Charismatic
Speaking in tongues is of the Devil. Therefore no true Christian would do such a thing, only the unsaved.

Hyper-Purest
You must agree on secondary issues with me or your not a very good Christian. e.g. KJV only people, Sacred name people

Hyper-Works
Trying to earn God’s love by doing things for him. Results in frustration and an inability to see God’s plan clearly.

Legalism
Being bogged down with a lot of extra unbiblical laws which prevent you from serving God in the freedom he gave you.

Liberalism
Taking the word of God too symbolically. Resulting in you falling into all the bad things in life that you would have missed had you interpreted it more literally. This can also prevent you from becoming a child of God.