The capacitor provides NEGATIVE FEEDBACK.
If we remove the capacitor, when the base "moves down", the collector "moves up." In other words the signal is inverted.
When the capacitor is fitted, we have to consider the circuit in a slightly different way. We have to start with the collector of the output transistor because it has more "power" and then go to the base.
When the collector voltage "moves down" the right plate of the capacitor moves down and the capacitor charges and tries to pull the left plate down too. This is the opposite effect to the signal moving through the transistor.
This means the capacitor is working against the action of the transistor.
The capacitor will have more effect on high frequency signals while the low-frequency signals will be affected less.
Because the capacitor is working against the natural flow of signal through the circuit, it is called NEGATIVE ACTION or NEGATIVE FEEDBACK.