"Empty triangle" is a term from the game of Go (Wei Qi/Badouk). It refers to the shape made by three stones as shown below:
.......
..oo...
..ao...
.......
(No stone at the point marked a, but see below)
It is a generally bad to form this shape with your stones, because it is overconcentrated, and doesn't have enough liberties. However, if the opponent has a stone at a, this is no longer the empty triangle. Instead, it is the filled triangle, which is a very good shape. So, obviously, if your opponent makes the mistake of making an empty triangle, you should not, for (almost) any reason, play at a.