The basic plot of the first game, avoiding spoilers as much as possible, is that Joel has been tasked with transporting Ellie across the country in the midst of an ongoing outbreak of a fungal infection that—for lack of a better term—turns them into zombies.
Actually, there is a better term for at least one variant of the zombies, and it’s playfully teased by this trailer if you have the captions on with “ominous clicking” showing up long before a Clicker makes a blink-and-you’ll-miss-it appearance in the gross, mushroomy flesh.