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When a charged particle loses energy, it creates a tiny ripple in the electromagnetic field. This is what light is made out of: The billions of tiny ripples created (mainly) by electrons around atoms changing their orbits and causing a little twang in the field around them. The wave created will spread out, as all waves do; but the higher its frequency - the more energetic the event that created it - the more it can go in one direction without being diffracted; visible light has a high enough frequency that most of the time it looks like it is just travelling in a straight line.
The direction of the movement that created the photon - this blob of light - will be at some angle to the path it is travelling, and the wave motion of the photon will reflect this; this is what is called polarisation. For a visual image of this, imagine waves travelling along a cord strung between two points; relative to the line of the cord, the waves can go either left and right, or up and down, or at some angle in between. In the first place, this angle - the polarisation of the wave - will simply depend on the angle at which the cord was plucked. However, if the cord passes through a slit then only the waves which are parallel to the slit will get through unhindered; waves which are exactly perpendicular to the slit will be absorbed entirely. Waves at intermediate angles will get through, but the component of their motion which is perpendicular to the slit will be absorbed and the wave that emerges the other side will be of a reduced size, and polarised in line with the slit.
Most light sources produce unpolarised light, since they include billions of electrons constantly firing off at random in all directions. When unpolarised light passes through a polarising filter, about half of its energy will be absorbed. In standard polaroid, of the sort found in polarising sunglasses, the filtering effect is the result of long polymers in the material, all aligned the same way. These polymer molecules absorb the component of the light with which they are aligned; the light that emerges from the other side will all be polarised in line with the filter. Any given photon stands a chance of passing through which depends on how close its polarisation is to the angle of the polariser.
Polaroid filters are not the only way that light becomes polarised. Light reflecting off water (or any other shiny but non-metallic surface) will be partially polarised; this is because the component of the light which is perpendicular to the surface is inverted by being reflected, and interferes with itself destructively. This is why there is a point to polaroid sunglasses; they are designed to cut out glare by removing light which has been polarised by hitting shiny surfaces.
Some materials have a more subtle effect on light passing through them. Optically active substances rotate the polarisation of light passing through them, while birefringent materials refract light by different amounts depending on its polarisation. The classic example of this is the mineral calcite, which produces clear double images by splitting the incoming light into two streams with complementary polarisations. Less obviously, see-through plastic is very often birefringent; it has a property known as photoelasticity, which means that its birefringence depends on mechanical properties such as the strain put on the material. The best way to see this effect is to place the plastic between two crossed polarisers - that is, polarisers (polaroid sunglasses or a polariser for photography, for instance) aligned at right-angles so that all the light which gets through the first is blocked by the second. Between the polarisers, pass some clingfilm, tape, a CD case or some other transparent plastic thing. The two components of the polarisation being slowed down (refracted) by different amounts get out of phase with each other, and the interference effects caused by this mean that the light which gets through is spectacularly colourful, with the colour of each part depending very sensitively on the stresses and strains on the structure at that point. Besides looking very pretty, this has practical uses in analysing loading in architecture and related fields.
There is a good deal more that could be said about polarised light; it is, for instance, often used to illustrate subtle features of quantum mechanics. For one thing, an examination of the behaviour of two photons with complementary polarisations shows that it is misleading to think of the polarisation of any photon as simply being aligned along a particular axis. Further analysis of such photons, as in Bell's Theorem, suggests that the universe is non-local in nature, meaning that subatomic particles appear to influence each other faster than we might expect Einstein's Theory of Relativity to permit. However, a detailed examination of the quantum nature of light is beyond the scope of this piece.
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