It is called a plane wave because it doesn't vary in the x and y directions, if the propagation vector is along the z direction.

So, across all of any xy plane at any instant the E field has the same (vector) value and so does the B field. That plane of constant E and B seems to move forward at the propagation speed.

it is called a TEM (Transverse electromagnetic) wave because both the E field and the B field vectors are in the xy plane which is transverse to the direction of propagation. There is no part of either vector in the direction the wave travels.

There is no such thing as a plane wave in real life because a plane wave never ends, but lots of waves are very close to plane waves, or close enough.