Capacitors in amplifiers
"unwanted ac signal" is a bit confusing - but not wrong.
The ac voltage drop across the emitter resistor RE is - indeed - in some cases "unwanted".

Why? Because the ac voltage drop across RE (caused by the ac current through the transistor which is identical to the output current caused and controlled by the input ac voltage at the base) acts as a negative feedback signal. As a consequence, the ac voltage gain would be reduced to approximately A=-RC/RE.

If we want a larger gain value the feedback effect for ac signals must be cancelled - but the DC feedback effect (caused also by RE) should be retained (for better stability of the DC operating point).

Hence, the resistor RE must be ac-wise shortened using a sufficiently large capacitor CE.

But note: In same cases we want to have "some" negative feedback also for ac signals (better linearity, better stability of the gain value). In this case, only a part of RE is bypassed using a capacitor CE (in practice: RE consists of two separate resistors).