Favors are tasks you can do for other inmates to raise their opinion and earn cash. Declining favors will make that inmate lose opinion of you, causing them to raise store prices and attack you on occasion, but accepting a favor and later abandoning will decrease their opinion of you even more.
Current favors are distraction, beat-up, item return, and find item. Money is given immediately upon completion of the favor.
Distraction requires you to cause a fight at a specific time, such as lunch or evening role-call. This can be achieved without making the guards hostile if another inmate attacks you first, due to a low opinion of you.
Beat-up requires you to attack a certain inmate. The location or time does not matter.
Item Return requires you to find a specific item from a specific inmate and remove it from the inmate or their desk. Although the item will disappear, there must be an empty slot available to pick it up.
Find Item requires you to gift a specific item to them.