The show will follow the events of the first game, where grizzled survivor Joel is tasked with smuggling teenage girl Ellie out of a quarantine zone and quickly finds himself teaming with her to fight off the Infected (basically zombies) and rogues on a cross-country trek. There is a chance the production will touch on The Last of Us Part II, although that likely depends on demand.
While TV show adaptations of games are quite rare (many will have flashbacks to the old Super Mario and Legend of Zelda cartoons), this might be a good fit. Naughty Dog's games from recent years have frequently focused on relatively mature storytelling, with serious subject matter and characters that evolve over time. In theory, Mazin and HBO won't have to work so hard to translate TLoU's narrative to something non-gamers can appreciate.
This is also a beginning for Sony. The company's TV studio co-president Chris Parnell told Hollywood Reporter this is the "first of many shows" it intends to develop with PlayStation Productions. Whether or not that comes true likely depends on the quality of this first outing and the suitability of other games to the format, but don't be surprised if more of the PlayStation catalog finds its way to your TV.