I started to post this last night and got distracted by work, never finished it...
Your TV will have a native resolution - that specific number of pixels across and high that it actually uses to draw a picture. As an example, it is common for "720p" HDTV's (LCD, plasma, DLP) to have a resolution of 1366x768. For these fixed pixel displays, all sources are converted to that resolution for playback. (There are some cases where a 1:1 pixel mapping mode is used to display 720p data on 768p displays by simply not using the top and bottom two dozen rows, but that's an exception to the rule.) The problem early in HDTV's development was poor scalers and deinterlacers in the TV's doing this conversion, leading to disappointing results. Progressive scan DVD players (which deinterlace DVD's 480i video to 480p) have been around a while now (since around 2000 or 2001, at least), but a few years ago manufacturers started going one step further and adding scalers to the players so that you could choose to output the video at 720p or 1080i as well as 480p. The goal was to let you get your output video as close to your display's native resolution as possible, thus minimizing (or perhaps even eliminating) the scaling done by the TV. If the player had better scaling than the TV, the result would be better picture quality.

The OPPO 970HD will allow you to toggle between 480i, 480p, 720p, or 1080i output (although disc playback must be stopped to change resolution). The 981HD will allow 480p, 720p, 1080i, or 1080p (480i is presently not an option, and I don't know that it ever will be due to the way the video signal is routed through the player).