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In mathematics, the discrete Fourier transform (DFT) converts a finite sequence of equally-spaced samples of a function into an equivalent-length sequence of equally-spaced samples of the discrete-time Fourier transform (DTFT), which is a complex-valued function of frequency.
In DSP we convert a signal into its frequency components, so that we can have a better analysis of that signal. Fourier Transform (FT) is used to convert a signal into its corresponding frequency domain. Initially people used DFT (Discrete Fourier Transform). Later on FFT (Fast Fourier Transform) was created. If N samples are present, DFT takes N^2 operations while FFT takes only N*log(N) operations.