The Fourier transform is a mathematical operation that decomposes a function into its constituent frequencies, known as a frequency spectrum.
Simply put, the Fourier Transform coverts a time-domain signal to a frequency signal. The composite waveform depends on time, and therefore is called the time domain representation. The frequency spectrum is a function of frequency and is called the frequency domain representation. Each value of the function is a complex number (called complex amplitude) that encodes both a magnitude and phase component. The term "Fourier transform" refers to both the transform operation and to the complex-valued function it produces.