TV resolution isn't measured in dpi (dots per inch) per se. Talking about dpi (or more accurately, ppi -- pixels per inch) is more a reflection of the device you're looking at (how large the pixels are -- they'd be huge on a jumbotron (inches per pixels, for instance) vs your smartphone (400+ ppi).... It's confusing for sure..

The letter p in 720p and 1080p stands for "progressive" and the letter i stands for "interlaced"

1080 itself stands for a screen resolution of 1920x1080 (and 720 means 1280x720).

Here's a good explanation:

https://www.youtube.com/watch?v=H_o5h5SK_70