If we’re just talking about a leather jacket, then mostly minor cuts and scrapes. The lining provides a little protection from impacts, it won’t save you from a baseball bat, but it does make blocking unarmed strikes a lot less unpleasant.
Some motorcycle gear has fiberglass plates, this stuff will take a baseball bat, tire-iron, or hitting the pavement at low speeds. It’s not fun, but it will save a lot of damage. I don’t think the fiberglass will protect against being stabbed, and (probably) won’t do anything about a gunshot. That said, fiberglass was the basis of some early flack vests, and some motorcycle gear is reinforced with kevlar so, your character could get lucky.
If you’re talking about historically, leather armor is a little different. Leather would be boiled in water, and then formed into the desired shape before it hardened. Once hardened, it would function as a low quality slab of stuff between you and anyone trying to kill you, or a substitute for scale. So, again, impacts, cuts, scrapes, and minor penetration. But, I’m not sure how well it would hold up against someone trying to stab through it, (that probably depends on how thick the slabs of leather are, and what’s trying to run through them.)