Usually refers to a video format consisting of either 720 active lines of progressive video or 1080 active lines of either progressive or interlaced video.
Digital broadcasts with either 1,080 active scan lines in interlaced format (1,080i) or 720 lines in progressive format (720p) as defined by the Advanced Television Systems Committee. (See active scan lines, ATSC, and interlaced scanning.)
High definition in projectors relates to the quality of the image the higher the resolution (number of lines that make up the width and the number of lines that make up the height), the better the image quality. Projectors tend to use 1024 * 576, 854 * 480 and 1280 * 720. a resolution of 1280 * 720 would normally be found on more expensive projectors and is a High Definition image.