The FFT is a complex beast, not something that can be comprehensively discussed in a single text box (I know accomplished engineers who have taken multiple semesters of classes studying topics that boil down to Fourier Transform analysis). Because of the nature of Accelerate framework's tasks, it too is a non-trivial discussion topic.
I would suggest reading Mike Ash's Friday Q&A on FFTs, where he covers some basic use of the vDSP functions to get FFT values, as a starting place.
See this DSP Stack Exchange answer for discussion on convolution and cross-correlation.