First of all, I'm not sure that I understood you but when light is reflected off a medium at Brewsters angle the light is polarized PARALLEL to the surface of the medium (I'll always be talking about the electric component), if the medium is a table and the light hits it from left to right, then the light that's reflected will radiate only along the "in out" axis = from your side of the table to the other side.
The reason for this is simple, the EM field of light always propagates perpendicular to the direction of the light. Now let's split it up into two components, the "in out" (normally symbollized by a dot) and a second component perpendicular both to the "in out" and to the direction of the light (if the light was going to the right, this component would point up). Now, when light hits a medium it's electric field oscillates the electrons in the medium which generate another EM field in the direction of the oscillation, this new EM field is the reflected light.
When the light comes at Brewsters angle, the reflected light always makes a right angle with the incident ray(this is one way to calculate BA with Snells equation), because of this, the direction of the reflected ray will be the same as the second component of the incident light described above. Since they're in the same direction, the electrons that this component oscillates cannot contribute to the new reflected ray because, as I mentioned above, none of the EM is in the direction of the ray! So only the "in out" component can generate the reflected ray and that means the this ray will be polarized parallel to the surface. This Wiki describes it well.
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Please tell me if that wasn't clear!