HDMI is audio and video (so you can use your monitors on board speakers if it has them without the need to wire it up from a sound card). DVI is video only. Both are digital signals so they give the best video quality.
D-
Sub is VGA, an old analogue signal standard, you can't use this on a digital only monitor.
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The term "D-Sub" stands for "D-Subminiature," which is a type of connector. D-Sub connectors were created in the 1950s, and they are still used in modern computers. They are shaped like a sideways letter "D," with one side slightly longer than the other.