Looking over the Gunslinger class for the first time and it says they start with a "battered" gun. What does this mean? The way it's written, it seems like this is supposed to be a specific condition for items, but I can't find any kind of description for it.
The description of a battered gun is just the description that is written in the Gunslinger class, you don't get the standard 1000+ gp worth weapon, you get a modified one.
It's flavour text. The gun looks worn and beat-up. "Battered" is not a condition (but the gun does have altered game effects described later in the text, as others have mentioned).