rsync is a tool for making a copy. It mirrors files from one place to another, in one direction only.
unison is basically like rsync except it goes both ways. It copies in both directions at once and tries to merge the changes from both sides. Imagine you had an extra copy of your music library on a computer at work. You add one song at home, and a different song while at work. You could use unison to copy the new songs from each computer, thus synchronizing both copies of the music library.
You could say that Syncthing is like unison except it can sync between more than 2 computers at once. And unlike rsync and unison, it can run continuously, syncing changes as they happen. Some people use it to replace Dropbox or Bittorrent Sync, but it has a lot of uses.