I've got an electric guitar with a bridge that looks like this:

I'm about to restring it and I need to know what those adjustable screws are for? Do I need to worry about them? As far as I can tell they aren't for a whammy bar.
they are for adjusting the height and length of the individual saddles. its part of how your action is set. the saddles are where your strings go across and is what sets them for intonation. you can leave them alone and if you don't know the proper way to adjust them are better off leaving them alone.