Film term, if you're not a filmmaker, but in the film industry, specifically, in Hollywood:

Getting paid to read screenplays, often for a movie star's own production company.

For example, Fortis Films is a company whose only purpose is to find a decent script for Sandra Bullock. It's got office space on a studio lot, and some twentysomething with a cell phone who has a pile of scripts on his desk. Is it his job to read them? No. It is his job to recommend scripts to Sandra and her agent. So he hires his friends (starving screenwriters) to read the screenplays at $50 a pop, while he goes and does lunch with the folks at El Dorado (Alec Baldwin's production company) and wonder why the lackeys at LivePlanet (Matt and Ben) won't return their calls. The starving screenwriters are happy to scope out their competition and earn some rent money.

Why is it called coverage?
Because the person recommending scripts, not having read them, is covering his ass by making sure that on the off chance that Sandra asks about a script, he can get a summary from his buddy and make it look like he's a productive human being.