This lecture focused on the frequency domain. More specifically, transferring an image into the frequency domain, performing some sort of filter on it and then transferring it back to an image. Some types of filters can be accomplished much faster in the frequency domain than by using a regular filter.
A discrete Fourier transform takes data from the time domain and transforms it into the frequency domain. The frequency domain contains information about the frequency and amplitude of the sine waves that compose the original data.
This is the same as the discrete Fourier transform except that it is performed in two dimensions.
You can represent an image by adding up many sine waves. This sine wave data can then be expressed in the frequency domain.