how can you have it go in multiple directions?
Hang on, hang on. Let's get somethings straight about polarization. There are lots of different types of polarization of waves.
Let's confine this discussion to just electromagnetic waves. The direction of E-M polarization is defined as the direction of the E-vector, which as others have said is perpendicular to the direction of propagation.
Individual waves have amplitude, wavelength and
one oscillation axis for the electric field vector. This is known as
linear polarization of
one wave.
Then we can have the superposition of
multiple waves, each with randomly orientated amplitude, wavelength and electric field vectors. This is a bunch of
unpolarized waves (plural). You can also have
partial linear polarization in which one E-vector axis is enhanced relative to all the other E-vectors.
Another special case is
circular polarization where
two electric field vectors are generated with the same wavelength and amplitude going in the same direction and 90 degrees or 1/4 wavelength out of phase. The superposition of these
two waves creates a circular polarized wave, in which the net electric field vector
rotates about the direction of propagation. In the general case where the wavelength and phase are constant but amplitudes are not exactly equal then it generates
elliptical polarization. So you can have more than just linear and random polarization.
