This is basically a summary of the tutsplus.com guide here.

Shape Modes (Top Row)

The effect will depend on the number of shapes and the stacking order of them, but the below table (again from tutsplus.com) shows a pretty good overview of what to expect:

Pathfinders (bottom row)

Divide is the most commonly used and splits the object into different shapes — at the points that the shapes overlap

Trim – removes the overlapping parts

Crop – uses the topmost object to trim away everything else