HD is actually a poorer resolution than most computer lcd screens (maybe netbooks are the exception). HD ready would mean you can plug tv components such as bluray dvd players into it and get their best output using the HDMI digital cable.

There may be more technically going on in the background (upressing the hd signal to fit the lcd screen?), but HD ready doesn't impress me for computer screens.

In other words, if you have a dvi cable, you have the best digital connection between the computer and the lcd screen. An HDMI cable doesn't get you more.