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. 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 (like the string's wave) but generally (and typically, in astronomy) 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. 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 (an arrangement of the wave's oscillation such that the direction is also oscillating in a circle). The latter rotates either rightward or leftward (according to the right hand rule), termed right-hand circular polarization (or RHCP) or left-hand circular polarization (or LHCP).