If we say that the light is traveling in the z direction, then unpolarized light has electric vectors that are randomly oriented in the x,y plane, but plane-polarized light has electric vectors preferentially oriented in one direction (for example, only along the x-axis).
Light consists of electromagnetic radiation, so it has oscillating electric and magnetic fields. Plane polarized light has a preferred direction of the electric field (along the x-axis, for example), so the corresponding oscillating magnetic vector would be along the y-axis.
Light is composed of discrete units called photons, which each have one unit of angular momentum, so it is also possible to have circularly polarized light about the z-axis (the direction of propagation). Plane-polarized light consists of equal parts of right- and left-circularly polarized light, so that the resulting electric vector is confined to a single plane.