I'm very green to CCTV, but with the research I've done, it seems D1 is the best quality most DVRs can record. My understanding is D1 is 704 X 480. On YouTube I see video from security cameras that are in 720p - 1080p. Are they using a NVR to get this quality?
Analog video is limited by the analog standards that have been in use since the 50s - usually NTSC in North American (525 scan lines, 483 of those visible) and PAL (625 lines, 576 visible) in most of the rest of the world.
For higher resolutions you need to use digital transmission of some kind - most common is network (IP) transmission to record to an NVR or hybrid DVR; less common is HD-SDi (Serial Digital Interface), which is based on a broadcast standard. HD-SDi currently supports up to 1080p (1920x1080, or 2MP resolution); IP resolutions are theoretically unlimited, although they do run into practical limitations of network speed. Still, there are cameras commercially available up to 29MP.
If most analog DVR's can only record up to 480 lines, what is the reason to get a camera better than 480TVLs if you don't plan to watch it live? Am I not understanding something?
It's got nothing to do with live vs. recorded - analog video is limited to about 480 lines (in North America), PERIOD.
I see a lot of pictures comparing 400TVL cameras to 600TVL cameras, but I'm not understanding how they are able to get the 600TVL images when using a DVR that records at D1.
One word: MARKETING. In the days where 480TVL cameras were pretty high-end, 280-380TVL was more common, and going with a higher number always meant higher resolution. Marketing has kept up that trend, and most people have bought into the idea that "more TVL is always better". Of course, there's always weakest-link theory and having a higher-TVL camera ensures that the camera's resolution will never be the weakest link in the chain... but as you've discovered, that only goes so far.