Other forms: kickbacks
A kickback is a bribe or payment that's given to someone as a reward for their help with something. If your cousin says she'll give you a pack of M&Ms if you help her steal candy from a neighborhood store, that's a kickback.
Illegal kickbacks are used to entice people into colluding in some criminal activity. It's a particular type of bribe in which the person receiving the money (or candy) and the person giving it are both participating knowingly in something illegal. This "illegal payment" definition arose from colloquial English, from that idea that the receiver of illegal profit "kicks" part of it "back" to someone who helped them obtain it.