Three main differences:

1. The i5 has four cores, so it can run four programs at the same time. Taking advantage of this requires you to have four programs that want to run at the same time, or alternatively one program (such as Photoshop) that can split its work into four parallel threads. (Useful for applying an edit to a large photo.)

The i3 has two cores. It also has something called "hyperthreading," which lets one core run two programs, so it looks like four cores - but this is less useful than four physical cores. It matters only when your workload can take advantage of more than two cores.

2. The i5 has Turbo Boost, which lets it run faster than its advertised speed under heavy load (until it starts to fry the machine, at which point it slows back down). The i3 doesn't.

3. The i3 is cheaper. It definitely gives you more "bang for the buck" at the chip level, since it was priced to compete with AMD's low-end offerings. Is the system-level price difference enough to matter? That's your call.

There may also be a clock speed difference when comparing two specific computers, but both chips are available in an overlapping range of speeds.

BTW, if you look this sort of thing up on the Web, be sure to get current info. The original Core i3/i5/i7 line was streamlined after its original announcement. The original line-up, for example, included two-core i5s. Confusing? You bet!

Added in edit: the article linked above, posted after I brought up the original thread to answer, is pretty good.