AMOLED is the abbreviation for Active-Matrix OLED, a type of display that is found in TVs and mobile devices, like cell phones. AMOLED displays actually pair part of a traditional TFT display with an OLED display. This allows them to offer faster response times than regular OLED displays, which can be prone to ghosting when displaying fast-moving images. AMOLED displays also offer greater power savings than traditional OLED displays.
Like traditional OLED displays, though, AMOLED displays may have a more limited lifetime, because of the organic materials used to make them. Also, when viewed in direct sunlight, the images on an AMOLED display are not as bright as what you'd see on an LCD.