Let's assume you want to buy a computer and are bewildered by all the terms. This guide should help you out with a glossary of a few key terms and how to rank them according to your needs.

megabytes, M, MB, RAM

These all refer to the short term memory the computer has for juggling multiple tasks. More is always better, but it's often cheaper to add more yourself later. The two major exceptions are when they give you a free memory upgrade, or you buy a Compaq machine (which is always painful to upgrade and the parts cost more).
64MB - Not enough for Windows XP
128MB - normal minimum size these days - should be OK
256MB - better if you want to edit pictures or movies
512MB - great for a power user, but overkill for your kids

gigabytes, GB

This refers to the disk space - or the amount of stuff you can hold. If your kids are interested in music, 20GB should hold around 200CDs worth of music.
20GB - most entry level systems have a disk this size it's fine for music & schoolwork.
40GB - this is a common upgrade option, because these disks are becoming relatively cheap. If you do a lot of photo editing, this would be a minimum size.
80GB - if you want to do video editing, this is the minimum size you need, but you'll still be pressed for space.

24X, 48X CD

The CD-ROM drive is often refered to by a multiplier so they say "24X CDROM", which means it can suck data off it 24X faster than a plain audio CD. This is not nearly as relevant as they make it out to be. When you have a CD/DVD writer, they often give you a set of numbers like "48/8/2", meaning 48X on reading, 8X on CD writing, and 2X on DVD writing. On any name-brand machine you buy, these numbers are not important enough to be used for comparison.

DVD formats

If you are just getting a machine which can read DVDs, then don't worry about this. If you are going to WRITE DVDs, then you must consider that writers come in a few formats, they are fighting for market dominance.
DVD-R - my favorite. All the DVD-R disks I've made have played in all my DVD players.
DVD+R - I think HP uses this. I think it is dying off.
DVD+RW - re-writeable DVD format. I think this is often a big waste, unless you use the DVD as a backup device and have a regular rotation through the disks so you can reuse them.

10/100 ethernet

Most machines come with an ethernet port today. If you have a cable (or DSL) modem in your house, this is what you need. If you don't, then you should get one, because you don't want two kids trying to each use telephone lines at the same time to get on the internet. To hook more than one computer up the the cable modem, you need a router/firewall and some cabling. These are about $80. Wireless is also possible, but more expensive. LinkSys makes some fine firewall boxes.

56K modem

who cares, see above

Schoolwork / music download / CD burning

128MB ram, 20GB disk, CD writer

Graphic arts, business user with lots of word docs and spreadsheets

256MB ram, 40GB disk, CD writer

Home Video editing

512MB ram, 120GB disk (or more), CD/DVD writer

And, do yourself a favor. Get a Mac.