Active matrix denotes a thin film transistor system in which each individual pixel luminesces on activation and the screen is drawn all at once each time it refreshes. Active matrix displays provide a more responsive image at a wider range of viewing angle than dual scan (passive matrix) displays.
Since the three colors in the pixels themselves are light, the screens don’t have to be backlit. The technology also enables the blackest possible blacks for a higher contrast ratio, given equal brightness.
Their construction makes AMOLED screens lighter as well as thinner, while simultaneously being much more durable. Their efficiency allows for reduced power draw. On the other hand, they don't last as long as IPS LCD's because the pixels don't retain their image quality as long, losing brightness over time.
AMOLEDs are typically used in portables like smartphones and tablets but manufactures are working to increase sizes up to those of large OLED TVs. AMOLEDs have also been used in flexible, transparent and practically unbreakable displays.
See a screen quality comparison video, followed by a durability demo: