Transitions are functions that move from the currently playing pattern to the next over a set amount of time. Or simple it allow you to gracefully change from one pattern to another.
The transitions themselves are defined in your editor when you boot it up. e.g. the Atom package has the transition functions defined within its source code. You can view the transition definitions at https://github.com/tidalcycles/Tidal/blob/master/BootTidal.hs#L23.