Can't Live Without Ours
DVR - I think it stands for Digital Video Recorder, is part of our cable set up. As a busy mom of 2, it allows me to tailor what my children are watching. We tape shows we want the kids to watch (Arthur, Dragon Tales, Blues Clues, etc...) and when we allow them to watch TV, we can go back and have them watch it. It works a lot like a VCR but ;so much better.
It also allows DH and I to tape our fav show -CSI. There are weeks we cannot watch it so we DVR them. On Fri nites, DH and I have our own little date nite with popcorn or dinner and a show.
It is an additional fee to our cable and if we wanted to, we could "move them to tape", I think. We never have to, though. We simply just "save until told to erase" which is an option we can change the save time to. You do have a certain amount of space but it is plentiful. DH can record his football games and watch them without interrruptions from the kids and fast forward commercials (or boring parts).
Like I said, we love ours and can't imagine life without it.
What your husband might also be referring to TiVo. That I'm not familiar with, sorry. I do know it works similarly to DVR (and I think came out first and is sold in stores) but that's all I really know.
Hope it was helpful,
Shark