Each gang has its own map. You will receive an invitation from the gang when you do great and earn lots of XP in their map.
Wharf Rats own The Docks
Killa Watts own Gotham Power
Carnies own Amusement Mile
Hazmats own Ace Chemical
Alley Cats own Crime Alley
When you quit your gang & level with another gang, all your data and progress for your previous gang is saved and will not be deleted. The best and fastest way to level up in your gang is to figure out which map you do your best in and stick with it.
The maximum reputation level you can obtain with each gang is level 10. At every 2 levels of reputation gained you will earn a catchphrase and on the tenth level you will unlock the symbol of that gang. Reputation is very difficult to gain and takes a very long time, you gain reputation after every game you play and according to how well you did regardless of whether it's your turf or not.
The percentage that the gangs have next to them is to do with how much of the islands (on the very left) they own.