AMOLED stands for active-matrix organic light emitting diode. It is a widely used display technology, Specially in portable devices like smartphones, tablets, smartwatches, etc. Amoled displays is just a type of OLED (Organic LED) where organic compounds forms electroluminescence material where Active Matrix refers to the method/technology to address individual pixels.
Unlike LCD, IPS displays OLED display pixels emits their own visible light thus do not require back-light. This allows to turn off black pixel which saves battery and gives virtually infinite contrast ratio resulting in vibrant pictures.
Amoled displays being active matrix allows for higher refresh rates compared to PMOLED (Passive-Matrix OLED).
PMOLED displays also requires relatively higher amount of currents for operation.
Amoled displays can have refresh time less than a millisecond.
Most flagship and higher end phones comes with amoled (if not oled) displays.
since black pixels on amoled displays can be completely turned off do not require any power, amoled displays allows for features like Always On Display (AOD) in which a small part of display is always displaying information. This allows user to see time, notifications, etc without waking up their device.