What does it mean "two plane thrust vectoring nozzle"?
This statement is using "plane" in the mathematical-geometric sense, which is of course very confusing when we talk about a part of a "plane" in the "flying machine" sense.

So, a "one-plane" thrust vectoring nozzle can only move up and down or left and right (typically up and down). So, this gives you pitch control using the thrust, without requiring airflow over the elevators. This is sometimes called "1D" thrust-vectoring, but it is also (confusingly) sometimes called "2D" thrust-vectoring (see the last paragraph).

A "two-plane" thrust vectoring nozzle can move up and down and left and right. So, this gives you yaw control without using the rudder in addition to pitch control. This is sometimes called "2D" thrust-vectoring, but it is also (confusingly) sometimes called "3D" thrust-vectoring (see the last paragraph).

In a two-engine aircraft, in both cases, you can add another "virtual" axis by having independent vectoring of the two nozzles, e.g. one up and one down, which gives you roll control. That is why, for two-engined aircraft, we sometimes talk about "2D" and "3D" even if the individual nozzles only can move on one or two dimensions.