What are the empty sockets on items for in Diablo 3?

I'm running across certain items that when I examine them say "empty socket".

I've tried searching Google to no avail. I'm assuming you can maybe attach something else to them? Can anyone explain what they're for? If you have links, I'll gladly take 'em so I can read up, too.

Solution 1:

"Empty socket" means you can attach certain gems to the item. Gems have various stats when found which will affect the stats that the item gives when equipped.

In act II you will find the "Jeweller". The jeweller will allow you to upgrade your gems (3 of each kind) to the same gem of a higher quality.

You will find more information about gems on http://us.battle.net/d3/en/item/gem/

Happy gem hunting! (Hint: for lvl'ing, equip a ruby in your helm for extra %experience from monsters)