From aa-asterisk.org.uk wiki
A "Direct Dial In" number ("Direct Inward Dial" in American parlance) is a number which traditionally connects directly to a nominated extension on a PBX. Typically used for assigning public telephone numbers to employee desks in companies.
Typically, a customer would ask for a block of 10, 100 or 1000 numbers from their CP and these numbers would be piped directly to the customer equipment, and the customer equipment would decide which extension to route them to.
DDI on analogue exchanges was very difficult to do, but the GPO and subsequently BT did offer the service. With the advent of digital exchanges and ISDN and VoIP, the setting up and use of DDI numbers has become relatively trivial.