Typically the Celeron has been based on the mainstream Intel CPU with a much smaller cache and possibly with some performance features removed. Since the cache makes up much of the die area for the CPU, that means they can fit more CPUs on a wafer and sell them for less; I remember some people claiming that Intel have sold mainstream CPUs where the cache didn't work as Celerons, but I've no idea whether that's true.
Some of the early Celerons weren't much worse than the mainstream CPU because the lost performance from the small cache could be made up by overclocking higher than the mainstream.
Celeron is not a platform, its Intels low-end processor family as one of the other posters said, I think you are confusing it with centrino mobile technology. Intel has three main processor families in the consumer level (busniss is different completley). Celeron, Pentium, and Core. These three families break into more specific family branches. Go to www.intel.com and you will get all information about thier technology, products, and all that stuff. Its a great website.
I heard that it's more of a platform than a processor. Can anyone elaborate?
The Celeron is simply a mainstream chip with things turned off, reduced cache, and reduced clock speeds to make it a budget chip. I think the "platform" thing you're thinking of is "Centrino," which is Intel's mainstream mobile platform (Intel Pentium M/Core/Core 2 CPU + Intel IGP + Intel wireless card).
As a side note, some Celerons are decent and some suck. The current desktop Celeron 400 series is decent if you want a very efficient single core. The dual-core Celeron E1000 series isn't so great as they have so little L2 cache that performance is much poorer than equivalently-clocked Pentium Dual Core or Core 2 CPUs. I'd also avoid the Celeron M laptop CPUs as they lack SpeedStep and will constantly run at full voltage and full speed and eat your battery much more quickly than a SpeedStep-enabled Pentium Dual Core or Core 2 CPU.