John 6:44 No man can come to me, except the Father which hath sent me draw him: and I will raise him up at the last day.

The word "come" used here simply means to be moved from one place to another. Just as a package is transported from point A to point B by a truck. The meaning of this passage is brought to light by looking at John 6:37 which states that a certain group of people are delivered to Christ by the Father.

John 6:37 All that the Father giveth me shall come to me; and him that cometh to me I will in no wise cast out.

Only those who are given to Christ by the Father will be delivered to Him. To be delivered to Christ, they must be moved from one place to another. We can find scriptural support for this in Colossians 1:13, which states that those who are delivered to Christ are translated, which is a synonym of being transported, from the power and authority of darkness into the power and authority of Christ. The word translated is used in Hebrews 11:5 to describe how Enoch was taken from this world so that he should not see death.

Colossians 1:13 Who hath delivered us from the power of darkness, and hath translated [us] into the kingdom of his dear Son:

See John 6:37 for comments on the proper understanding and usage of the rest of that passage.
An example for the word "draw" is that of John 21:6, when the fishermen were not able to draw in their net for the multitude of fish. When we use this to properly understand the drawing of God we find that only by the great power and strength of God the Father is a person able to be removed from the power and authority of darkness and place him into the power and authority of Christ.

Jesus states that no man "can come" except by the Fathers drawing. No person can be delivered into His power and authority, except by the Father's divine intervention. This drawing does not violate mans free will. In fact, it enables the person to exercise his free will choice at a later time.

Matthew 11:27 All things are delivered unto me of my Father…

The word "delivered" means to give into the hands of another. Thus, we come into Christ’s possession by being delivered to Him only by the Father, and not by our own means.

Other than the references presented here, this event is also described as the washing of regeneration (Titus 3:5), being born of water (John 3:5), being baptized into death with Christ (Romans 6:3&4), eating the bread from heaven (John 6:50&51,58), eating the flesh of the Son of man (John 6:53&54,56,57), and adoption (Ephesians 1:5)

This event takes place without the knowledge of the person. There is no physical, mental, or moral change that takes place. It is only a spiritual status change. A legal adoption takes place where the person becomes a child of God, although disobedient and unlearned at first.