Probably the biggest contribution that the HUD gives is the velocity vector. Basically it shows where you are physically going. If it is level with the horizon, the you are neither climbing or descending, regardless of airspeed and everything else. Remember how you had to learn which attitudes hold you level for different airspeeds in the T-34 (nose high for slow, nose low for fast, etc)? You don't have to do that anymore. Plus, since you're looking at it and looking outside at the same time, your instrument scan is easier. By the way, if the VV is on a ridgeline, that's where you're going to hit the ridge. Keep an eye on it.
That's a pretty dumbed down version, but you'll see what I mean when you get there.