This is the question which might have crossed your mind at some or the other moment in time. Well, nothing wrong with it as elevators are a serious piece of machinery which requires its fair share of respect and adulation.
In order to understand how the elevators or lifts actually work, we must first understand how many types of elevators are there actually. Well broadly and commonly speaking an elevator is classified on the basis of propulsion system or the powering mechanism used for its operation.
There are four types of the mechanism used for powering an elevator or a lift and this also forms the basis of their nomenclature:
Traction Elevators:

Traction elevators are of two types geared and gearless. Geared traction elevators are used with an electric motor. These motors can either be AC or DC type. They use worm gears for mechanical control, basically, they control the elevator movement by using a steel rope over an drive shaft connected to a gearbox, this gearbox is eventually connected to the high-speed motor.
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AC motors were widely in use owing to their low cost and economic feasibility. These motors serve the purpose perfectly where the low-speed application is desired. However, as the height of buildings increased there was a need for faster elevators as having a low-speed option was no longer viable. Hence the practice of using DC motors for driving the elevators came in to picture. These motors were typically powered by a stand-alone device called an MG set or a motor generator set which has the capability to operate in both AC and DC mode. It also powered other systems of the elevator hence separating the power supply to the elevator from that of the building. This also meant that there would be no power spikes in the building due to the operation of the elevator.