The Seiko Museum Ginza's definition: "An escapement is a device that rotates a wheel in fixed intervals while continually applying intermittent force to maintain the oscillation of the regulator."
Two jobs in one mechanism: it releases the gear train a step at a time, and it feeds a small push back to the oscillator to keep it going.
Why it is needed at all, in Grand Seiko's words: "If the force from the mainspring were transmitted directly to the hands, they would rotate at an uncontrollable speed, making accurate timekeeping impossible… the escapement regulates the rotation of the gears to ensure precise timekeeping."
The audible tick of a mechanical watch is the escapement releasing and locking.