Why we connect a capacitor in series to the base to amplify AC signals in BJT?

Coupling capacitors block any DC component of the signal being amplified.  This prevents the signal source from affecting the DC bias of the BJT.

You can in fact amplify without the capacitor but in some cases you need a capacitor so the circuit bias is not disturbed. A driver is needed in general because the speaker impedance is very low and requires power. The circuit preceding the diver is used primarily to provide gain and operates at low power.

I'll try an explanation that I think gets the point across simply.

BJT amplifiers need some method of setting up the quiescent bias voltage for the BJT base. For the the usual example case, this is done with two resistors making up a voltage divider. (There are other ways.)

Let's say, just as an example, that the base bias voltage is supposed to be +2V and that the power supply is +9V. R? and R? form a voltage divider and you select the values so that the divided voltage is about +2V. Then you hook up the base to that. If the values of R? and R? are low enough, the BJT base and emitter resistor won't load it down much.

But what about the signal source you now hook up? It might be producing a signal that is centered on 0V and swings up and down ± 0.1V around that. If you hook that up directly to the bias point, it will probably mess up the signal source (distort it) and/or mess up your designed bias point, or both.

Putting a capacitor in between these two allows the capacitor to automatically develop a voltage on it that is exactly the difference needed. So in the above case, after a very short time, the capacitor will be charged up to about 2V. And when the signal source wiggles the "lower" end, then the other end of the capacitor will wiggle by the same amount... but with +2V added (like if a battery were there, almost.)

When the circuit first starts up, the capacitor won't be charged and there will be some momentary distortion as things "settle down." But very quickly the capacitor charges (on average) to just the right voltage difference. Once that happens, things work very very well.

The capacitor should be large enough that this stored voltage on it won't change much in the time it takes the signal to wiggle up and down from the source. If the source's rate of change is too slow (low frequency), then the capacitor's stored voltage will "droop" while supplying current on one half of the cycle to the BJT base circuit. And that will affect what the BJT "sees" as a signal and distort it. So the capacitor needs to be large enough that this effect is small so that it doesn't matter much.