In battle, the backgrounds are a texture on a 3d plane, and is treated like all textures are, with some sort of filtering, usually bicubric. Outside of battle, the backgrounds are bitmaps, not textures, and are treated as such. It's just the steam port that is lousy from SE's side.

Mod is short for modification. HD is an abbreviation for high definition. A HD mod is a high-definition modification for the game. Presumably, this guy used a mod that replaced the background bitmaps with versions that have been upscaled with a reasonably good filter.

Mods are usually third-party additions to games, and a lot of games do not not officially support modding, which makes installing them a bit technical.