1080p is one of the HDTV formats. It means the image has 1080 lines of "vertical resolution", i.e. 1080 pixels from top to bottom. The p stands for progressive, which means that each frame is a single full-resolution image, unlike 1080i in which each frame consists of two interlaced fields.
1080p video usually has 1920 lines of horizontal resolution, making a total image size of 1920x1080 pixels (2,073,600 total). The aspect ratio is 16x9.
1080p can be specified as 1080p24, 1080p25 or 1080p30 — the additional number refers to the number of frames per second (fps). Traditionally, PAL countries use 25fps, NTSC countries use 30fps. 24fps is the frame rate for film, making this an ideal format to use for film conversions.
In the future it is envisioned that 1080p50 and 1080p60 will become the production standards, combining the benefits of progressive scan with a higher number of total images. Currently, bandwidth considerations make these formats impractical, but this could change with more efficient codecs.