Fast Fourier Transforms (FFT):   

In SoundHack, as well as many other sound analysis/transformation programs, an FFT and inverse FFT (IFFT) are used to calculate the approximate frequency composition of a sampled sound. 
Sound is analyzed via a frame by frame basis, a frame being a spectral "snapshot" of a moment during the sound. These "snapshots" are strung together to comprise a breakdown of the frequency components of a sound and how they exist over time. In some of the applications in SoundHack the window size of an FFT may be chosen.   
Fourier analysis may be generally described as the representation of a sound's frequency components as a sum of pure sinusoidal waves (Truax, Handbook for Acoustic Ecology: 51). An analysis of a sound's frequency components is taken at a steady state to give an approximation of that sounds spectrum. As most natural sounds are spectrally dynamic, one single Fourier analysis could not possibly represent a sound in sine waves. By 'windowing', a Fast Fourier Transform takes several of these approximations and strings them together to better predict a sound's spectrum over time.