For example, a simple polarizer could be a grid of thin metal wires whose spacing is smaller than the wave-length of the incoming light. For the component of the E-field parallel to the wires currents can be induced freely along their length, and so the grid behaves much like a solid metal plate and reflects that part of the wave. For the component of the E-field perpendicular to the wires, significant currents can't be generated (since the wires are thin) and that part of the wave passes through.
[1] https://en.wikipedia.org/wiki/Polarizer
[2] https://en.wikipedia.org/wiki/Polarizer#Wire-grid_polarizers
It depends on the type of polariser.
The type used in LCD displays and 3D cinema glasses absorbs, that's why everything looks darker through them but they don't look like mirrors.
A polarising beam splitter reflects one mode and passes the other. It looks like a half-mirror.
Where goes the energy of the orthogonal component of the field? Absorbed by the polarizer, reflected, ... ?