I believe what you are looking for is the "quick launch toolbar". (for the rest of this note, I'm going to assume you are running Windows XP - if not, let us know). Here's a quick try to help you out - if none of this works, post back with some more details.
Two possible problems - first, if the whole toolbar is gone, right click on any black space on that stripe at the bottom of your screen. You'll see toolbars as one of the options that pop up. Go under toolbars and check the quick launch toolbar.
If the toolbar is still there, just that the Explorer icon is gone, the easiest way to get it back is to go under your Start menu and find another Explorer option. Click on that, and while holding down the mouse, drag it to the quick launch area.
As I said, if none of this helps, post back with lots of details and people will hopefully be able to help more.