High Definition boils down to better picture quality, but to really understand the difference you need to understand a little about how a TV actually displays an image, so let's start from the beginning;

Similarly to film, TV uses multiple static images flashed on the screen at a high rate of speed, somewhat like the familiar home made cartoons where multiple slightly different images are drawn on multiple sheets of paper and then quickly flicked through. The biggest difference is how the actual images are shown; where films display multiple complete solid images, like a slide or photo, a TV 'draws' these images as a succession of horizontal lines. 

This works because the eye and TV screen have what is called persistence; the eye can see an image for longer than it is actually there. When the eye sees something it 'remembers' it for approximately 1/24th of a second, so if the eye sees 24 or more successive images per second, it doesn't see any flicker; basically the new image appears before the eye 'forgets' the previous one. The actual screen's persistence is what allows the drawing of multiple lines to produce a whole image; the screen remembers the first line almost as long and it takes to draw the rest of the image, so, if we draw these lines across the screen fast enough the eye will see a whole image, and if whole images are flashed on the screen fast enough, the eye sees fluid motion, therefore by repeatedly drawing lines across the screen fast enough, the eye is fooled into seeing fluid moving images.

The TV signal type first broadcast was developed using the motion picture industry's discovery that a minimum of 24 images per second are required to fool the eye into seeing fluid flicker-free motion and the readily available 60 cycle per second power source in a standard wall electrical outlet.

Standard Definition signals contain a total 480 horizontal lines of picture information per image. The inventor of the Television system decided to use the wall outlet's 60 cycle per second signal to trigger the TV's image repetition. To this end he halved each full image into 2 separate 'fields', each containing 240 lines of picture information with each respective 'field' containing either odd or even numbered lines. To display a picture, the TV first draws lines 2,4,6,......476,478,480, then 1,3,5,etc., this is called an "Interlaced" signal and it is now more commonly referred to as 480i (480 interlaced lines). 60 half images or 'fields' per second produces 30 full images per second, this is fast enough to surpass the no-flicker point and using the wall outlet signal for triggering makes building the TV easier and cheaper.

Progressive Scan simply means that 60 Full Images per second are shown on the screen rather than 60 half images. By drawing all the lines each time instead of only half of them, without skipping any, the lines for each image are considered to be drawn in a progressive pattern rather than an interlaced one. This is referred to as 480p; 480 progressively scanned lines. This effectively doubles the number lines per second, thus doubling the detail resulting in smoother and crisper images.

High Definition signals simply have more lines spaced more closely together, either 720 or 1080 (the lines are longer too, but that's not pertinent here). Currently 480i, 480p, 720p, 1080i and 1080p signals are available, where, as above, the numerical value refers to the actual number of picture lines and the letter refers to how the lines are drawn on the screen, 'i' meaning interlaced and 'p' meaning progressive.

Since the more lines drawn per second the better the detail and overall image quality, 1080p signals are currently the best quality available and offer an increase in image detail of 450% over standard definition 480i signals.