What is a common-emitter bjt push-pull output stage?
A BJT (NPN in this example) connected in common emitter configuration looks like this:



Putting two of these with opposite polarity together is a push-pull stage:



The name comes from the fact that the output is actively pushed and pulled in both polarities.

There are a great many details about how to drive the two transistors so that they each turn on when needed, but not both turn on to fight each other.  Just getting the DC quiescent operating point right isn't trivial.  This is sometimes called biasing.  That would be good to look up.

Also look up class A amplifier, class B amplifier, and class AB amplifier.  These classes have to do with the overall strategy of when each of the transistors are intended to conduct.  The classes are a tradeoff between smooth transitions and wasted power.

Those details are beyond your simple question, but this should give you things to go look into.