There's a great thread about this in the main forum area, something like "I got a new HDTV" - loads of good info (you can pretty easily discern the BS from the facts).
Very briefly I = Interlaced, P = Progressive (think non-interlaced)
When you talk about a TV generating X frames per second, in a P based set, an entire frame reference is drawn for each of those. So for example a set that generates 30 FPS Progressive is drawing 30 FULL frames every second.
An Interlaced set - using the same metric - draws 1/2 of the frame during the first 1/2 of frame reference, and the other 1/2 during the later part.
So it's generating 60 *fields* per second, to make up the 30 frames per second. Since a single viewable frame is drawn in two parts, there can be a little flicker as the first 1/2 of the frame fades (while the 2nd 1/2 is being drawn). Under fast motion, there can also be some leading/trailing edge artifacts because of the same reason.
In the end analysis, you're still talking about 1080H lines, but two different ways to render them. In general, a P scan produces a more solid frame, but in motion, it's barely detectable.