Q. What is their relation with gain? What are the factors affecting frequency response of an amplifier?

Some amplifiers should be "flat" across a band of frequencies. In other words, for every frequency within the band, the amplifier should have equal gain (equal response). For frequencies outside the band, the amplifier gain will be much lower. For other amplifiers, the desired frequency response is different. For example, perhaps the amplifier should have high gain at two frequencies and low gain for all other frequencies. The frequency-response curve for this type of amplifier would show two "peaks." In other amplifiers the frequency-response
curve will have one peak indicating high gain at one frequency and lower gain at all others.

The frequency response of an a.c. circuit is limited by the reactive elements (capacitance and inductance) in the circuit.  This is caused by the fact that the capacitive and inductive reactances vary with the frequency.

In other words, the value of the reactance is determined, in part, by frequency.  A totally resistive circuit would have no frequency limits. However, there is no such thing as a totally resistive circuit because circuit components almost always have some reactance. In addition to the reactance of other components in the circuit, most amplifiers use RC coupling.

This means that a capacitor is used to couple the signal in to and out of the circuit. There is also a certain amount of capacitance and inductance in the wiring of the circuit. The end result is that all circuits are reactive.