Polarization is the orientation of waves to a particular direction: not the direction the waves are traveling, but a direction perpendicular to that. For example, a taught string disturbed, producing a wave-motion traveling down the string consisting of a (traveling) displacement of the string in a particular direction, e.g., up/down, left/right, or along some diagonal. Such a case is polarized in the particular direction, but sound waves are not polarized: it is an oscillation of pressure at each point rather than a displacement of something in some specific direction.
Electromagnetic radiation (EMR) is naturally polarized (in the manner of the string's wave) but typically beams of EMR include displacements in all directions, having no direction as particular and the EMR is termed unpolarized, reserving the term polarized for any tendency towards particular directions. Thus EMR can be partially polarized, just a little, or a lot. Astronomical EMR with such polarization include maser radiation, synchrotron radiation, radiation from active galaxies, pulsars, the cosmic microwave background, and light scattered by dust. Magnetic fields affect EMR polarization and polarimetric observation often aims at learning about such magnetic fields. Polarization of EMR from dust suggests non-spherical grains that are aligned, e.g., by a magnetic field. The polarization may be detected in the absorption of starlight, in which case, a number of stars showing identical polarization suggests it was caused by an interstellar cloud in the foreground rather than from the individual star systems.
Polarization can be linear (as above, e.g., like polarized sunglasses) or circular, in which the wave's oscillation such that the direction of displacement is oscillating in a circle. On a string, it would be a traveling spiral. The rotation is either rightward or leftward (according to the right hand rule), termed right-hand circular polarization (or RHCP) or left-hand circular polarization (or LHCP). Circular polarization is equivalent to two simultaneous linear polarizations, out of phase by a quarter wavelength. Such simultaneous linear polarizations can also be out of phase by other fractions of a wavelength, which produce additional kinds of polarization.