Not sure what it stands for but the term is used here in Ireland for Direct Dial Numbers. .
For example, if a small company with say 20 employees, has only 6 phone lines, it …can purchase say 20 DDI numbers as well from the telephone company, and provide one Direct Dialling Number to every employee. In this way customers and suppliers can ring people in the company directly, and the company uses 20 phone numbers with only 6 phone lines. .
A PBX is needed in the company to distribute the incoming calls to the correct telephone handset. .
Perhaps it stands for Direct Dial Incoming ? ( Full Answer )