Integrated means a chip on the CPU/motherboard. Dedicated means a separate card or chip handling it.
Integrated is slower than modern dedicated graphics cards, but also consumes less power, which is a large benefit on laptops. Recently integrated graphics have gotten a bit better with intel's sandybridge processors. They're i3, i5, or i7s that are numbered in the 2000's (ie "Intel Core i5 2540M", or "Intel Core i7 2600K").
AMD has some processors lined up that will have pretty impressive graphics built into the CPU, but they aren't out yet, so I won't go into detail.
If you're on a desktop, then it's really best to get a graphics card. With a laptop you have to compare high costs and the ability to play more recent games at higher settings (or at all, in some cases) against better battery life and cheaper costs. Laptops can't upgrade their graphics later down the line, so you have to think about it some.