Frequency response is the measure of any system's response to frequency, but is usually used in connection with electronicamplifiers and similar systems, particularly in relation to audio signals. For example, a high fidelity amplifier may be said to have a frequency response of 20Hz - 20,000Hz ±1dB, which tells you that the system responds equally to all frequencies within that range and within the limits quoted. As such it is not a measure that is very useful in terms of the quality of reproduction, only that it fulfils the basic requirements needed for it.
A related term is bandwidth, but that has both a more tightly defined meaning, and a broader application.
Frequencyresponse is the measure of any system's response at the output to a signal of varying frequency (but constant amplitude) at its input.
Once a frequencyresponse has been measured (e.g., as an impulse response), providing the system is linear and time-invariant, its characteristic can be approximated with arbitrary accuracy by a digital filter.
Frequencyresponses curves are often used to indicate the accuracy of amplifiers and speakers for reproducing audio.