A pure mate is when there is exactly one piece checking the enemy king and exactly one piece guarding every one of his escape squares. This pure mate happened to me in a bullet game some days ago. This is probably not my first pure mate, but it stood out to me in that I found it with three seconds on the clock (considering I was playing on mobile with no premoving, I was saved by the bell), and i was also a little proud of its interesting symmetry. I am certainly not proud of my play in this game, which was sub-par and ended in me spending far to much time on silly junctures.
For those interested in pure mates, there are two sub-classes which are almost more interesting, the model mate, a pure mate in which every one of your pieces takes part, and the ideal mate, in which every piece on the board participates in some way/
In general, endgame mates such as RKvsK are not considered to be pure mates although some are so by definition.