By noticing that your fingers get wrinkly in the bath, you are observing an important phenomenon known as osmosis. What happens in osmosis is that water moves across cell membranes to try to reach a balance point with all the stuff that is dissolved inside of a cell. Our bodies, which are made of cells, are mostly water. The liquid inside a cell, called the cytoplasm is really kind of like seawater. It's basically salty water, with lots of other things dissolved in it, like dissolved proteins, and genetic material. The borders between cells, or cell membranes, are not perfect seals. These cell membranes will allow water to leak across and into or out of cells. Water will flow across the cell membranes whenever there is an inequality of water versus dissolved stuff on the two sides of a cell membrane. So if the cytoplasm of a cell is like salty water (lots of dissolved stuff in the water), and you put a cell into regular, fresh water (not a lot of stuff dissolved in the water), the water will flow until there is equality of dissolved stuff on either side of the cell membrane. So, in the example I just gave, water would flow into the cell placed in fresh water because the water would flow until there was equal "saltiness" on either side of the cell membrane. As the water flows into the cell, it dilutes the "saltiness" of the cytoplasm, as the water flows out of the medium surrounding the cell, it slowly increases the the "saltiness" of this area, so eventually the two sides of the cell membrane will be equal in saltiness--this situation is called equilibrium.

See the following web site for further information on this topic:
http://www.straightdope.com/classics/a2_317a.html

http://www.randomhouse.com/catalog/search/34535145.html

So when you place your hands in water and your finger tips appear to shrink what is going on? Well this one is a little tricky because you usually associate getting wrinkly with something that is shrinking, but that is not the case here. Instead, the salty cells inside your finger tips are swelling up with water because the freshwater outside your fingers is less salty than the "water" or cytoplasm inside your fingers' cells. Therefore,
water flows into your fingers' cells trying to make the "saltiness" balance out. There are tiny little connections under your skin with other parts of your internal finger. As you finger swells these connections become tight and it makes it look like your finger is wrinkled (and shrunken), but really your finger is swollen.

Try a little experiment at home. Take a raisin and soak it in warm water.
What happens? Why?