Centrex (Central Office Exchange Service) is a PBX-like service providing switching at the central office instead of at the customer's premises. Typically, the telephone company owns and manages all the communications equipment and software necessary to implement the Centrex service and then sells various services to the customer.
The Centrex service effectively partitions part of its own centralized capabilities among its business customers. The customer is spared the expense of having to keep up with fast-moving technology changes.