It include in the circuit to provide a low reactance path to the amplified ac signa. As shown in  fig below. it is not connected in series like a coupling capacitor,  instead it is connected across the emitter bypass capacitor CE is used to prevent negative feedback in the emitter circuit
Emitter bypass capacitor|Single Stage Transistor Amplifier
Emitter bypass capacitor|Single Stage Transistor Amplifier


very simple,negative feedback involves feeding back a portion of the amplifier output signal to its input circuit. Further the signal feed back in such a manner that is opposes the input signal. The removal of bypass capacitor results in an increase in the amplifier's input resistance, a reduction in its voltage gain and an increase in the output resistance is a step in the right direction for voltage amplifier. However a reduction in the voltage gain and increase in the output resistance are generally undesirable effects. Yet there are some advantages offered by these sacrifices .  First even though the voltage gain is reduced but stability is increased parameters(e.g its gm) . Second the increase in the collector-to-ground output resistance makes our approximation of Rout equal to RC even more elastic