I will give you a simple easy explanation:
In the Hard Drive you save all kind of stuff, from games to pictures to music, to whatever you may want.
The RAM, is the one that allow, those games and music to play, the more memory your computer has the better the games will play, and the faster the computer will be, now since I know Kids, I have 2 of my own, try to get a computer with at least 160gb hd, and at least 1gb of ram, that will do, now see the following links pick one and let your kids enjoy, or why not give them your computer and keep this one.. I did that.. jejejejeje.. A smart Dad..
the first one is 529 bucks, nice and way enough and has a monitor.
The second one does not have a monitor but you can always get a cheap one any where, or why not go shop any computer store, any computer around 600 bucks will do. Trust me, look for 2 things: HD > 160gb, Memory >= 1Gb. the rest is pure bla, bla, bla.