The Garden of Eden was the environment that God created for a relationship with Him to take place. Adam and Eve's responsibility was to dress and keep it. They were put there, not to do nothing, not just to pluck fruit off a tree, not even merely to receive eternal life, but to take care of the Garden.
Dress means "to embellish." This may seem a little strange, but Adam and Eve were to take care of it so well that it would become better than it was when God gave it to them. We like to think of the Garden as being a place of absolute and perfect beauty. Instead, since God told them to "dress and keep it," it seems that it was not complete. It had only been started. What He had done was certainly beautiful, but He wanted them to carry on and finish it.
Keep means "to guard" or "to preserve." If they did not work to dress the Garden, God is telling them, it would deteriorate. That is the way of all things physical, they degenerate if they are not maintained and taken care of.
There are spiritual lessons here. We have been invited into a relationship with God. Like any relationship, it must be worked on to make it increasingly tighter and more productive. We are to "dress and to keep" the relationship. We are not in the Garden, certainly, but we are in the relationship. To do this, we must use and grow in the Holy Spirit. The relationship is the key to accomplishing this. If there is no relationship, there is no Holy Spirit working in and with us, no chance that we will ever grow in the Spirit, and no way we can be close to God. The relationship is the key.