A stall, technically, is a departure of turbulent airflow over the top of the wing due to an extreme angle of attack. When this happens the wing no longer generates lift as designed. In most "everyday" aircraft scenarios the most common reason for a stall is a combination of insufficient speed and too high a nose pitch. Aerobatic aircraft including fighter jets can encounter stall scenarios in other ways, including intentionally (several maneuvers involve intentional stalls; the 3-D equivalent of intentionally entering a skid in a car).
When taking off, an aircraft typically does not exceed the maximum angle of attack for its current speed; if it did, the aircraft would stall and likely crash. The aircraft instead accelerates to a speed in excess of the forward stall speed of the aircraft, and then gently pitches upward to gain altitude. To the average passenger, especially a first-timer, it may not look or feel "gentle" to have the aircraft pitch 15-20 degrees up in the air, but during that maneuver the AOA remains very shallow.
To assist heavier aircraft (or those designed for faster cruise speeds) in getting off the ground quickly and/or at a lower speed, the flaps can be positioned in a moderate setting, often specifically designated as a "take-off" setting, to increase the lift the wing generates at lower speeds. This happens through a combination of increasing the effective upper surface of the wing, and also directing the airflow leaving the wing downwards. In a "clean" configuration (the most aerodynamic setup for cruising, which includes no flaps), the minimum speed at which the wing can still generate lift will be higher.