The 1080 bit refers to the picture resolution. Both 1080i and 1080p have the same picture resolution. This means there are 1920 pixels of the image down the screen and 1080 pixels across the screen. This equates to 1920 x 1080 pixels on the screen in total. For some reason the industry only uses the number of pixels across the screen as a indication of the picture resolution. 1080 picture resolution is the best you can get at the moment. Other types of resolution are 720p (1280 x 720), 480p (720 x 480) and 480i (640 x 480).
The i and p bit indicate the way the image is put on the screen or the scan type. The i stands for interlaced. Interlaced scanning is an older method of putting the picture onto the screen. It is more common in older style CRT TVs. The p stands for progressive and is the modern way to put the picture on the screen. The interlaced format draws the odd numbered lines on your screen first, i.e. 1, 3, 5, etc and then it draws the even number lines i.e. 2, 4, 6, etc., while the progressive-scan format draws all the lines at the same time.
The picture comes on the screen very quickly but the progressive technique is smoother and less flickery than the interlaced method. Thus it is claimed that the picture will be better using the progressive method although it is hardly noticeable to the eye. It may also be better for fast paced action movies or rapid changes to the image but, again, it is debatable whether the eye will pick up on this.
Mike my guess is your TV is 1280X720. It will accept 1080i signal but would probably look better if you went into it 720 (less processing going on).
Hope that helps a bit.
