Rackets and Earn

These are the illegal operations currently operating in a district. Each district has two rackets. You have to complete a series of objectives to take over the racket which you can then assign to one of your underbosses. Rackets increase your underboss' total earn which in turn increases the amount of kickback you'll receive. Earn is basically the total amount of cash that flowing to your underboss. Increasing their max earn unlocks more type of favors or upgrade existing ones. Take note that in order to reach an underboss's highest possible earn, you have to hand more than 3 districts to him/her, which ultimately means that you have to kill one of your other underbosses. However, with equal distribution of districts, you can access all favors from each of the three underbosses, save for the last two ones. Still not a bad deal.
Taking Over Rackets

Racket bosses always work behind the scenes and to draw them out so you can target them, you have to damage their racket's earnings completely. It's possible to max out the damage to a racket and lure out the boss even if there are still objectives remaining in the map. I will always recommend clearing all objectives since most of them have extra cash that you can steal. These objectives will seem repeatable with some variations but the usual tasks are listed below.

1. Interrogate informants. You can then kill them for extra cash or spare them to add to the racket's total earn once it's taken over
2. Kill Enforcers (if you don't do this, surviving enforcers will become the boss' personal bodyguards when he appears in the racket hq)
3. Sabotage small operations
4. Steal stash or other operations' earn
5. Tail or destroy vehicles. This involves following red vehicles that appear in the mini-map and killing its passengers
6. Kill the racket bosses' smaller gang units
After dealing enough damage, the racket boss will appear in the racket's hideout. These areas are heavily guarded so you can plan what kind of approach you want. Usually a stealth approach is recommended to decimate the numbers of the guards in the area and for you to move into more advantageous positions. Racket bosses won't attempt to escape even if you made noise and the firefight starts, which makes it more convenient. Upon reaching the boss, you can usually just lob a grenade or two to disable him then either spare him for more overall earn or kill him for instant cash.

Optional Missions

After taking over a racket, you'll notice that when you hover the pointer over it on the map, you'll see an amount. For example, 44000/70000. That means that it's current earn is 44000 but you can increase it up to 70000 tops. These can be done by doing the lieutenants' optional missions, under the underboss you assigned the racket to. That means, to max the earn for rackets assigned to Cassandra, you have to do the repeatable optional missions for Emmanuel. For Vito rackets, you have to do Alma Diaz's missions, and lastly for Burke, you have to complete optional missions provided by Nicki. This will usually involve stealing something from the Dixie Mafia in the Bayou and delivering it to the racket. Though repeatable, its worth doing this since maxing the racket's earn also counts toward your underboss' total earn.
Kickbacks
Kickbacks is the cut that you receive from your underbosses from their earn. These become available automatically after some time has passed. You'll normally get a notification that your kickback is ready and you can also see them in the map. Early in the game, you have to manually drive to the underbosses' HQ to collect your kickback. However later on, as you increase Vito's earn, his Consigliere associate's service can be upgraded to collect kickbacks for you as well - anytime, anywhere.