Here is Wikipedias definition:

In electrodynamics, circular polarization of an electromagnetic wave is a polarization where the tip of the electric field vector, at a fixed point in space, describes a circle as time progresses. If the wave is frozen in time the electric field vectors describe a helix along the direction of propagation. Circular polarization is a limiting case of the more general condition of elliptical polarization.

They are horizontal polarization, vertical polarization, and circular polarization. Use the link below on antenna theory and see some examples and gather more information.

Basically, polarization describes how the E-field is moving when it leaves the antenna.

In horizontal polarization the signal moves in a horizontal fashion (-).

In vertical polarization the signal moves in a vertical fashion (|).

In circular polarization the signal moves in a circular fashion (O) with either left-handed or right-handed rotation.

Now, when you want to talk to someone using horizontal or vertical polarization you want to match their angle of polarization exactly for the strongest signal.

Cross-polarization is radiation orthogonal to the desired polarization. For instance, the cross-polarization of a vertically polarized antenna is the horizontally polarized fields.

This is important to know because when you are setting up something like a satellite connection. In order to allow more signals through the satellite transponder within a fixed bandwidth and with decreased interference, the satellite makers alternate the polarization between adjacent transponder channels. (-|-|-|-|-|-|). Two adjacent channels can be "shoved right up against each other" and will interfere in a minimal way if they are polarized oppositely. Since interference affects their customers, satellite vendors are very touchy about proper polarization, and monitor gaps, called "guard bands" to ensure that you are properly aligned.