1080p is essentially what was defined as high definition in the late 1960s when Sony measured what resolution was required to produce cinema quality in the home (around 2k by 1k pixels) - currently approximated by 16:9 1920 by 1080 pixels.
Until high definition discs arrive there has been little need for true high definition displays, as in the pursuit of quantity over quality the broadcasters generally opt for 720p. However, Blu-ray can easily support true high definition (perhaps we should call 720p intermediate definition to avoid confusion) and now that the launch is approaching many manufacturers are developing full 1920 by 1080 pixel progressive capable displays. Current examples include 54" and 57" TFT panels from Samsung with 8ms response and Sony and Apple both make 23" TFT panels at 1920 by 1200 pixel resolution.
Remember that whilst 720p may seem impressive compared to 480i, it's not such as step up from PAL (576i) or Secam (800i).