Well, do ya, punk?
Auto image correction, whether in Picasa (source of the question) or in Photoshop is a quick way to (sometimes) improve your image. Luck doesn't really come into the picture though, as the Undo button can always fix this one-step action.
Fortunately though, it usually does benefit your image, or at the very least, does nothing all that noticeable.
Most of the time it seems to focus on the contrast of the image.
As you can see, the difference between Picasa and Photoshop is minimal. However, the advantage with Photoshop is that you can Fade the result in the case it seems too extreme.
Quite often though, it also tries to remove a colour cast from the photo as well. Often (in my pictures at least) this tend to add quite a lot of blue to the image - often where it really doesn't belong.
Normal and Blue'd as separate links.
In a few cases, typically those shots with a small number of colours, it goes in a very bizarre direction.