What is PC2-3200 MB/sec, DDR2 SDRAM ?

I want to upgrade the memory on an HP A1312n Media Center computer. It comes installed beside 512 MB installed, and I can go up to 2 GB if the installed memory is replaced. The HP site scheduled the speed supported as PC2-3200 MB/sec. Will PC3200 400 MHz work? What is the ideal for tally 1 gig of memory?

What is PC2-3200 MB/sec, DDR2 SDRAM ?

PC2-3200 will work, but PC-3200 will. The difference logically is that one is DDR and the other is DDR2, and you need DDR2. PC2-3200 is pretty uncommon and hard to find, so newly get any PC2-4300 or PC2-5400/5300, either will work, they will basically slow down to work at the speed needed in your system.
DDR 400 and PC3200 are duplicate thing. Your system take DDR2, so the pc3200 is not an option, as the slots an pinouts of ddr and ddr 2 are different.