My best guess is that the development of forest root structures, combined with microbial, animal, and insect action, makes the soil more porous and absorbent. This allows rainfall to be captured and "reclaimed" by the soil, with excess trickling down into the aquifer. Simultaneously, the dense canopy provides shade to slow the effects of evaporation.

By contrast, a barren soil would become hard and compacted, and much of the rainfall would simply wash away or be lost to evaporation.

Again, this is one man's educated guess. I'm no expert, and it's quite possible I'm way off the mark.

I think the trees try to keep a reserve of water around them, instead of letting it go back into the ground. Some anecdata - my family due to risk of falling decided to cut down some trees. Mere days after that the sewage flooded the basement. The trees were apparently keeping a reserve of sewage water around their roots that got released once they were cut down, flooding the basement.

Multiple trees could keep that water around releasing it once there is too much water, thus forming or preserving aquifer. Not to mention they reduce evaporation.

A cursory search for "forest aquifer" returns a number of relevant results. A couple of accessible and interesting ones:

http://en.wikipedia.org/wiki/Pine_Barrens_%28New_Jersey%29

http://files.hawaii.gov/dlnr/cwrm/publishedreports/eco1469_a...

Bare ground results in erosion whereas a forest slows the movement of water, shades it and allows it to sink into the ground.