Videos on DVDs are generally stored at 1280x720 resolution. It is slightly more complex than that, but it is not really worth going into details. DVDs will never store videos at 1920x1080 resolution because DVDs do not have the storage capacity for movies of that resolution. DVDs can store roughly 8.5GB of data. Blu-Rays on the other hand can store between 25GB - 50GB of data.
A DVD movie will be stretched to fill a 1080p screen. When this happens video will look bad because the video filling a larger resolution screen without adding any details. An analogy would be to take a 4' x 4' square blanket woven with yarn, and then stretch it so that it becomes 8' x 8' square blanket. When this happens the yarn strands will be pulled apart from and you will start to see holes in the blank. Something similar happens when you stretch videos.
Watching a 720p video on a relatively small tablet that has a 1080p will not look too bad because on a physically small screen the "holes" in the video does not appear to be very large so it will look okay. Play that same DVD movie on 52" HDTV and it will look terrible, but playing the DVD movie on a 15.6" laptop with a 1080p screen will look much better compared to the 52" HDTV, but not quite as sharp on a tablet with a 1080p screen.