An agent is the person who carries out all the steps to find dates for an artist in a concert hall, a club, an event... in exchange for which, he receives a percentage (about 15%) on the fee he has negotiated.
There is not necessarily a need to establish a written contract with a booker, but it is always advisable to sign an agreement in order to avoid any misunderstanding. Looking for more gigs? You don't know how to find an agent? Would you like to become an agent for a band?