What Is The Difference Between 1080i And 1080p?

In theory, 1080p is better than 1080i due to the fact that with 1080i, the image is sequentially "painted" across the screen between the even and odd numbers of lines, that is at least on a traditional CRT. With 1080p, the image is displayed "all at once", so the pictures appears smoother, especially for faster moving images. However, with LCD's and Plasma's, they are progressive by nature which makes that sort of redundant.

A good place to start to learn more about the difference between the two is this website here.

Another great article that goes into more depth can be found here.