Interlaced format is the old original video format used with analog TVs. A frame (480 lines/frame, 30 frames/sec) is split into two fields (2 fields per frame) and displayed alternately - odd and even fields, 240 lines each, 60 fields/sec. With video from a video camera each field is captured 1/60 sec apart, so with movement in the frame the odd field will move relative to the even field. Progressive format outputs the full frame (480 lines) as one entity 60frames/sec. DVD players have to convert from the interlaced fields on the DVD to the progressive frames, some do it well others not so well. Digital TVs also de-interlace, again some well others not so well.
All DVDs have 480 vertical line resolution (thats what the "480" means) - so none have 720 or 1080 vertical resolution until a new HD DVD format becomes available - perhaps in a few years. There are a couple DVD player models (Bravo and Samsung) that upconvert DVD video to HD output on a DVI port, but this is not as good as true HD video.
For regular DVD players like your Denon, the player outputs either 480i or 480p, depending on your selection of interlaced or progressive on the DVD player setup and also depends on how you have the DVD player hooked up. If you use composite (yellow RCA connector) or S-video (black DIN connector) you will only get interlaced 480i. With component (3 RCA connectors, red/green/blue) you can get 480i or 480p. Progressive can be higher quality than interlaced with some video material (especially film-based movies) due to reduced artifacts in motion scenes. Interlaced may appear softer, but it depends on your TV. To support progressive (480p) format you need a digital TV (usually an HDTV) model too - regular old analog TVs are interlaced only and progressive mode won't work at all with them. Since you have a Pioneer plasma, its card will actually convert interlaced to progressive (since the plasma display is always progressive) so you may notice little difference between the modes - its really comparing the quality of the de-interlacer in the Pioneer vs the Denon.