Windows can run more than one monitor, and it can put them together so they "run into" each other, however it can not do this with full screen applications. You are able to have 1 full screen application per monitor using just Windows.
Eyefinity allows a full screen application to run across more than one monitor, meaning you can have full surround by angling the two side monitors slightly, making games more immersive, or you can make for a much larger screen at higher resolution by having each straight, which would make games look prettier, and films look better.
Imagine you have 3 32" each monitor is at 1920x1080. You could them monitors side by side to have it at 5760x1080 on a much larger screen