When polarized light hits a polarizer, what happens to the polarization which is not transmitted? It is typically said that in polarization of light only those waves can pass through a polaroid which has a plane of vibration parallel to the axis of polaroid.  My question is: what happens to the other waves (the other polarization)?
 A: Light that is not transmitted is either absorbed or reflected.
Wire grid polarizers tend to reflect. Polarization beam splitters separate the two polarizations in different directions. Polymer based ones absorb it i believe...
A: In general light that does not pass a barrier, a wall for example,  is absorbed.The energy is turned mainly  into heat and also chemical bond breaking etc.
The part of the light beam that does not have the correct polarization for the polaroid  will be absorbed in the same way.
A: Just to add to Anna v's answer and Aanel's answer which are both admirably pithy and correct.
Polarisers making use of the Brewster angle deflect the light of the "blocked" polarisation, rather than absorbing it. The "blocked" light actually passes into a refracting, the unblocked light is reflected off and redirected to the output. Polarising beamsplitters such as the Wollaston prism do something similar: you are making use of the different behaviour of the Fresnel equations for the $s$- and $p$-polarisations to divide the light into two, orthogonally polarised beams. Polaroids and other simple polarisers mostly absorb the blocked light, which is why you often have to calculate a damage threshold power to avoid their being heated to destruction by the absorbed  polarisation.
