Definition of High Definition:
High Definition is largely a fluid term, taking the shape of a lot of different containers, with the only real meaning being something with a significantly increased picture quality and clarity based on the resolution of the monitor in question. For this reason, High Definition is, in reality, a synonym for high resolution.
High resolution means more pixels in your screen, which leads to a remarkably more clear picture. There are some standards now that allow a more concrete resolution of what it means to have an "official" HD display monitor, even for your PC.
The following are the standard definitions for HD video, which is able to be displayed on monitors of slightly varying native resolutions, some being standard for computer screens, other for TV screens, but they are to a large degree interchangeable because they all work to display these resolutions of video:
1280x720 - aka 720p
1920x1080 - aka 1080i
1920x1080 Progressive - aka 1080p
The "p" and "i" after the resolution denotes either Progressive or Interlaced scanning, respectively. Progressive has been proven to the the faster, clearer picture, less prone to blurring, and therefore has won the title of the "standardized" best possible resolution for HD broadcasting at 1080p.
For your PC, high definition means taking your computer to the next level when it comes to playing video games, watching movies, and watching HD online video. HD means that the screen will be 'widescreen,' so you'll be watching it as it was originally intended to be seen, uncropped, in the theater.
Since HDTV caught fire, video game studios and online entertainment companies have been focusing more and more on HD programming for a high resolution screen. So really, what it ultimately means is, if you don't have an HD monitor, you're missing out on a big part of the picture.
HDMI:
HDMI (High-Definition Multimedia Interface) is a compact audio/video interface for transmitting uncompressed digital data.[1] It is a digital alternative to consumer analog standards, such as radio frequency (RF) coaxial cable, composite video, S-Video, SCART, component video, D-Terminal, or VGA. HDMI connects digital audio/video sources (such as set-top boxes, DVD players, HD DVD players, Blu-ray Disc players, AVCHD camcorders, personal computers (PCs), video game consoles (such as the PlayStation 3, Xbox 360, and Wii U), AV receivers, and mobile phones) to compatible digital audio devices, computer monitors, video projectors, tablet computers, and digital televisions.
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