How does capacitor improves the performance of a circuit?

This depends on what kind of circuit you have. Generally, you cannot just add a capacitor to a circuit and 'improve it'. Probably, though, you mean an amplifier, anf by improve, you mean improved frequency response. In a transistor amplifier, you sometimes want increased gain at higher frequencies. By adding a capacitor from the emitter to ground, you create a low impedance path to ground for the AC signal. This lowered emitter impedance increases the gain of the amplifier, for frequencies where the capacitor looks like a low impedance, or high frequencies.