HDMI - High Definition Media Interface
HDMI is short for High Definition Media Interface. It is a standard for plugs, cables, video and audio devices.
HDMI is a digital cable designed to offer very good quality audio and video over the same cable. It's worth noting that not all products do a perfect job and the standards have changed dramatically over the years.
HDMI and HDMI cables has a particularly tricky habit of causing all sorts of weird issues with equipment. For example, picture not coming through on a display caused by a cable adhering to an older standard, or a blu-ray player with old firmware.
Some features released in newer standards: