Nothing. For your purposes, a Celeron is perfectly adequate. There are, of course, differences, but they are mainly in the amount of cache memory and FSB speed (both usually smaller, given similar processor speeds). These won’t much affect the speed of web browsing or other applications which don’t demand much in the way of processor overhead.
I suggest doing a search for “celeron benchmark tests.” These generally consist of running a program (like Quake III) on several different computers, usually with other specs (RAM, hard drive specs, etc.) all as similar as possible.
In general, a Pentium performs significantly better in long-running tasks (graphics rendering and such) while comparable Celerons may be slightly better at getting brief tasks in and out of memory quickly, but it’s all relative.
For web access, go for a good chunk of RAM and invest in a modem. The chip makes very little difference. (Just make sure the specific model of computer you’re looking at doesn’t have a history of random reboots, BSODs, and the like – the motherboard has more to do with that than the chip itself.)
