What does the p mean when speaking of a tv's resilution?

Answer 1

It means Progressive. As opposed to i, for interleaved. Progressive scan sets display their full resolution for every frame of video. Interleaved sets display TWO separate 'fields' for every frame- first they display the even numbered lines, then they display the odd numbered lines. ( much like normal NTSC TV broadcasts.) Because of persistence of vision, set with slower switching pixels will display a better picture with inteleaved video, as the eye will merge the two separate fields into one smooth frame. Progressive scan sets require a much faster switching speed because all of the pixels are switching together with each frame.