My brother brined a turkey for the first time this Thanksgiving and the breast meat was indeed juicier and tastier. I did a little reading on the process and I couldn't make the osmosis explanation jive with my background in chemistry.
You are dealing with two pots of saltwater (the brine solution and the interior of the cell) separated by a semi-permeable membrane, the cell membrane. Water wants to make things equal in concentration so it will always flow from the least concentrated to the most concentrated. If the brine is saltier than the cell, water would flow out of the bird until the saltiness became equal.
Eventually I found a more reasonable explanation, though it did come from wikipedia. The answer is not the level of dissolved salt, it is the level of dissolved solids. The cell has more total dissolved solids than the brine solution, so it is more concentrated. The water moves from the least concentrated brine into the more concentrated cells. And in brining it carries with it flavors and salt from the brine.
A reverse osmosis filter uses pressure to reverse the process, forcing water to move from the more concentrated dirty water to the least concentrated clean water. Otherwise the clean water would flow back across to dilute the dirty side.
Of course, I have gotten a lot more mileage out of this forum than I ever did from my degree, so I can now dismiss with the science and pursue the art.