What is meant by saying that one has a "frequency" representation of a signal?

Answer 1

Essentially, you are writing the signal as the weighted sum of pure tones. The frequency representation just shows the weights as a function of frequency. This is the same thing as the Fourier transform of the original signal.

Answer 2

It means that instead of describing a signal by what it does with time, it is expressed as a combination of frequencies (tones). Same answer; different way of specifying it.