Zarya is a particularly powerful tank in Overwatch. I think there are a few ways to play her and you can get pretty creative with her. Zarya is somewhere between a support, a tank, and a DPS hero. She is a very dexterous hero and should not be underestimated when thinking about adding her to your team.
The reason Zarya is such a powerful tool for this is her bubble shields. Zarya can place a shield on herself and one ally as they charge into battle and this will allow you to get in the thick of it with almost no risk for a few seconds. A few seconds does not sound like a lot, but a few seconds can start and end a fight.
Zarya needs to take damage in order to do more damage, so you want to put the shield up sometimes even after being shot at. Sometimes the shield can go up preemptively but with the fairly long cooldown you need to be wise about the placement. You should be fairly certain you are about to be shot, or even have received a small amount of damage before placing her bubble shields. It also helps a lot to not be the only tank on the field. If you have another tank to propel into a fight with the shield, even off-tanks like Roadhog or D Va, it can really help build that charge quickly.
Briefly stated above, her weapon charges with every bit of damage you take while shielding yourself and an opponent. A number will show up in the middle of your screen and it will go down as the battle continues. Therefore, it is extra important you are in the heart of a battle when charging your weapon. The higher the number is in the middle of your screen, the more damage you do so you do not want to waste it by charging off of some tiny stray poke damage and not have your shield when it is needed.
Zarya also has one of the best synergy Ultimates in the game. It pairs well with nearly every other ultimate because of its amazing crowd control. Watch the enemy group up, toss it in, and wait for D Va, Soldier, Tracer, Genji, McCree, Junkrat, Pharah, or probably a few other heroes I can't think of to clean up. Good communication and synergy is important in order to use it, but it's also the kind of Ult that can synergize the team for you because most players understand what it used for.
Back to the actual value you get from having a Zarya on your team. With Zarya, you have a peel, a shield for Zarya and one ally, a body block, good self-sustain because half of her health regens, great DPS with proper bubbles, and one of the best crowd control Ultimates in the game. She can be the glue that holds the whole team together. The synergy and uses she brings to the table can't be underestimated.