Your computer stores everything on the hard drive, which is a mechanical device that is like lots and lots of LP's stacked up. It's very slow though, so in order to speed things up, you also have RAM, which is memory on microchips. So what happens is that when you turn your computer on it copies bits of Windows that it needs into RAM. When you open a program like Word, it puts that into RAM. When you open a letter you've written, it grabs that from the hard drive and puts it into RAM so you can work on it and it'll all work faster. When you save the file, it saves it back to the hard drive again.
The problem with RAM is that it's 'volatile' memory. This doesn't mean it may explode, but that it loses its memory when the electric goes off. This is why if you're writing a letter and you haven't saved it yet and the computer crashes or the electric goes off, you lose what you've typed -- it's still just in RAM, and so it disappears.
More RAM means more programs and stuff can be put there at once. Things run smoother. 1GB is a good amount to have right now; XP works well with 512MB, and better with 1GB.
Because the hard drive actually stores everything, and the RAM is only a temporary thing, your hard drive is always far larger than RAM -- hence why I say go for 80GB or more.
The processor is the brains of the unit that conducts everything. The faster the clock speed rating, the better. Typically about 3GHz or so right now. Pentium is one name, but there are many different kinds. Pentium 4 is the current one, but it's quite old now. Pentium D is similar but is like having two brains on one chip. Same for the Core Duo and Core2 Duo processors.
All that above processors are by Intel though. AMD is another manufacturer that makes good chips (totally compatible with Intel's), and they're called Athlon typically. Again, the AthlonX2 processors is like the PentiumD -- two brains on one chip.