When elected officials accept kickbacks they're engaging in bribery or corruption.
Corruption is the abuse of entrusted power for private gain.
A kickback is a type of negotiated bribery in which a commission is paid to the bribe-take, in this case elected officials, in exchange for services rendered. The kickback may be money, a gift, credit, or anything of value.
The kickback is usually intended to encourage the other party to cooperate in the illegal scheme.