We can say that the components of ANY light oscillate perpendicular to the direction of propagation ... left and right, up and down, upper left and lower right, upper right and lower left, etc. ... any direction ACROSS the direction of propagation, just not forward and backward.
If the light is polarized, then the Ɛ-field (electrostatic) component of the wave can only oscillate in the polarized direction ... say, left and right across the direction of propagation. (The magnetic component is always perpendicular to the electrostatic component. So if the polarizer is left/right, then the magnetic component is up/down.)
Any light that doesn't oscillate in the direction selected by the polarizer gets absorbed in the polarizer, and doesn't come out the other side. That's why when you pass light through a polarizer, it comes out dimmer than it went in.
LASER light is always naturally polarized before it comes out of the diode or whatever is generating it. That's another advantage of laser light.