A video fade is when a shot gradually fades to (or from) a single colour, usually black or white. A fade is different to a crossfade, which is a transition directly between two shots rather than one shot to a colour.
The "fade from black" and "fade to black" are ubiquitous in film and television. They usually signal the beginning and end of a scene. The timing of the fades indicates the importance of the change in time and/or location between scenes — a slower fade with more time spent on black indicates a more significant end/beginning. A fairly quick fade to and from black could indicate a time lapse of a few minutes or hours, whereas a long drawn-out fade indicates a much bigger change.
Sometimes, two quick fades together can form a single transition similar to a crossfade. For example, a shot fades very quickly to white before fading back into the next shot. Such transitions usually last less than a second and are called a dip, e.g. dip to white or dip to black.
Note: In many production situations a fade refers specifically to an audio fade rather than video. In these situations a video fade might be called a mix to black or something similar.