How is it possible for the wheels of a car to be stationary while its engine is running?

How can a car's wheels not move while the engine is running AND engaged to the transmission? Shouldn't this damage the engine? For example, if I'm using automatic transmission and I shift into drive, the transmission should be engaged, right? But the car doesn't move unless I step on the accelerator even when the engine runs. Another example is when I'm driving up a steep hill and I step on the accelerator slightly. The engine will rev up, but the car will stay in place or even go backwards. How is this even possible without the engine, gears, axles, etc. getting destroyed?
 
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