Refer to figures.
When an aircraft stalls, this is because the wing's angle of attack (AoA) exceeds the critical angle, and the airflow begins to separate, as it does not have enough energy to maintain a boundary layer which “sticks to the wing". Somewhat similar to stalling the engine of a car (asking for more torque than the engine can give), it is when you ask for more lift than the wing can produce (by setting an angle of attack that is higher than the critical AoA).

The effect of power on a stall is dependent on the type of aircraft, but primarily:

• When an aircraft stalls, the angle of attack is high, usually meaning that the nose angle is high, and therefore the engines are pointing at least slightly upwards. They therefore are producing some upwards lift, reducing the weight the wings must support. This reduces the stall speed, as the aircraft can fly slower before running out of lift.
• If the aircraft is propeller-driven, then the slipstream from the propeller will increase the airflow over areas of the wing, which increases lift slightly in those sections, and this can decrease the stall speed also.