The mininum resolution for high definition is 1280x720, aka 720p High Definition. Any resolutions above that is high definition.

If by "hd movies" you mean blu-ray discs, they can play on your 1366x768 monitor in high definition and it will look decent. But some blu-rays with exceptionally clean transfers like the Dark Knight will really shine at 1080p (i.e. on a display that can do 1920x1080).

Whereas 1366x768 = 1,049,088 pixels, 1080p has almost twice the number of pixels-- 1920x1080 = 2,073,600 pixels. That's almost twice the amount of detail. So if you got some of the more recent blu-ray titles encoded at 1080p like Ironman, Dark Knight, Bourne Ultimatum, Transformers, Casino Royale, etc., those blu-ray discs look REALLY good on an 1080p display.