Let's have some alphabet soup. You know what an LED is. That's Light Emitting Diode. Usually you see them as little indicator lights and now as part of computer monitor backlights. Then there's OLED. That's Organic LED. Kinda self-explanatory in that there's organic material in there. OLEDs are thinner and use less power (and thus battery life). But they're still rather expensive.
And then there's AMOLED. Active-Matrix OLED screens use even less power. Colors are more crisp. They can be flexible. They pretty much mean you're not messing around. Don't ask questions. You want one.
And above is an even better description from Samsung VP Omar Khan, who should know a thing or three about displays in cell phones, given that the just-announced Omnia Pro and Omnia II have AMOLED screens.