It is their job to make sure that the actors auditioning are what the Director/ Producer are looking for. It is their job to the send the head shots to the Director/ Producer, and keep them informed on the which actor fits which role.
They are in charge of making sure that the right actor is hired for the right part. They are also in charge of negotiating deals with the actors and their agents, as well as managing the contracts that are signed by the actors.
Their job usually happens in pre-production, however it can sometimes extend into production as well.