It is difficult to make sense out of what exactly the state of Divine Union is, because human language and concepts are wholly inadequate to describe it. Essentially what happens is that when your soul is resurrected, the 'independent' part of you is now fully permeated with God so that there is no way to tell where God ends and you start. There are a couple of word pictures which the mystics use to describe it; one of them is a picture of a river (the soul) when it finally reaches the ocean (God). All of a sudden these two bodies of water which were once completely separate from one another start to mingle together and if you were to scoop up a cup of water, you would have no way of telling which of the water came from the river and which came from the ocean. The important part - and what separates this from a lot of Eastern mysticism - is that your substance is not annihilated, just penetrated and mixed with the substance of God. You become, in Peter's words, a partaker of the divine nature; divinized by participation in God.
Another picture which is used is that of a bar of iron. It starts out hard, cold, maybe covered with rust. But if you put it into a fire, first the rust burns off, then the bar of iron itself starts to heat up and glow because the fire is penetrating the iron in the same way the the Holy Spirit penetrates us. And even though the iron isn't turning into fire, it starts to act a lot like fire; it will burn you if you touch it. And if you leave it in the fire long enough, the iron becomes liquid and what you end up with is a substance which is still iron (but free of imperfection), but acts like liquid fire. And at that point you take on all the properties of the fire and you are completely pliable in the hands of God - just like Jesus was when He walked on the earth, manifesting all of the power and authority of God, and completely submitted to His will.
A third picture is that of a glass of distilled water. It has no shape, no color, no flavor, no smell of it's own. It is a completely neutral and pliable medium. If you take it and put it into a pitcher, it assumes the shape of the pitcher; if you throw it on the ground it assumes the shape of the ground. It has no tendency or desire to assume any shape except that which is imposed upon it. If you put food coloring in it, or add flavor to it, the water simply accepts these modifications without comment and is unable to claim that any of these properties are inherent to it or a result of it's own nature. You can see how this maps to the condition of a soul which is completely surrendered to and pliable in the hands of God. When you enter into Divine Union, you lose everything which you could ever have claimed to be your own, and you become a medium through which God can perfectly express whatever He wants to pour through you at the moment. And if you think about this, this is the way Jesus was. He said that he never acted of His own accord; He only did what He saw the Father doing, He only said what the Father taught Him to say. He spoke solely for the glory of the Father, never for His own. Jesus' will was always perfectly surrendered to the will of God, and when you enter into this state, you have surrendered your will to the point where you, properly speaking, don't have a will anymore; your will and God's will are one and the same and they can nevermore be divided or distinguished.
When you live like this, walking by the spirit is not like it was before - where you had to stop and listen for God and fight the tendencies of your flesh. When you live in Divine Union, you are in God and God is in you so thoroughly that you just automatically have God's mind and His understanding. In the words of Genesis 2 - the two have become one, and you essentially become a completely pure and submitted vessel which God can pour the unlimited vastness of His glory out through to touch both the Church and the lost just like Jesus did when He was here.
This is what the mystics aimed for and what they attained. And Jesus prayed in Jn 17:21-23 that everyone who believed in Him would enter into the same experience:
At the point where you enter into Divine Union, unity within the body becomes a non-issue, because if you are fully permeated by God, and I am fully permeated by God, then we are united simply by virtue of being permeated by the same God. And in fact what happens is that our souls beging to permeate one another; this is something which the mystics referred to as the interpenetrating union of souls - all of us mingled together with God and in God with one another.
This is what the mystics walked in; they reached this place. They walked around as conduits for the power and the glory of God with no impedence whatsoever from the soul. And they turned the world completely upside down. Some of these mystics were uneducated peasants - weak, frail, foolish vessels - but through their union with God they had such influence that kings and queens bowed before them. Their lives were fulfillments of Jesus' statement that we shall do greater works than He did, and Paul's statement that we can do all things - and that really does mean all things - through Him who is our strength.