Let Scripture answer, from our Lord's High Priestly prayer:
John 17:11-17 And I am no more in the world, and these are in the world, and I come to thee. Holy Father, keep them in thy name which thou hast given me, that they may be one, even as we are. While I was with them, I kept them in thy name which thou hast given me: and I guarded them, and not one of them perished, but the son of perdition; that the scripture might be fulfilled. But now I come to thee; and these things I speak in the world, that they may have my joy made full in themselves. I have given them thy word; and the world hated them, because they are not of the world, even as I am not of the world. I pray not that thou shouldest take them from the world, but that thou shouldest keep them from the evil one. They are not of the world even as I am not of the world. Sanctify them in the truth: thy word is truth.
What we can learn from this prayer, to help us be separated from the world:
1) That believers are physically in the world.
2) That our Lord desired us to be one in mind, as He was one in mind with the Father.
3) That we have been given His Word.
4) Because of His Word and the believers witnessing, the believer is hated by this world, just as Christ was hated in His day of ministry. Therefore, being loved by the world is not a good sign of ones faithful walk. We should always HONOR God and not be man pleasers.
5) Believers are not of the world. They don't act like them, they don't think like them and want no part in them, other than to see if God has done something for them.
6) Jesus Christ is no longer bodily in the world.
7) We should be kept and be keeping ourselves away from evil.
8) Believers are sanctified in the Truth of God's Holy Word. The word "sanctified" means to "set apart for Truth", in this context, v.17.
Therefore, point number 8 is the clearest reason as to our being set apart. We should come out of the world and separate ourselves to Truth. We can not please Him by concerning ourselves with the physical or fleshly things, we Honor Him through the spiritual things, by worshiping Him in Spirit and Truth. Then going out into the world and defending this Truth.