Business internal dialing refers to the dial structure within a single business entity, and is sometimes referred to as Virtual Private Numbering (VPN) or Private Numbering Plan (PNP).
This structure allows users a shorter number sequence for numbers within the same building or company (or in theory, a whole of any size, the only real restrictions come from regulations).
CIBC in Toronto used 6-XXXX (XXXX denotes the last four numbers of the full 10 digit number) for numbers originating from 416-784-XXXX numbers and 7-XXXX for numbers 416-780-XXXX. All external numbers used 9-416-XXX-XXXX sequence. This sequence is part of the Nortel Networks Meridian 1 Communications Systems and Meridian Mail system.
This sort of system is fairly common in different types of PBX Systems, with these being a few examples:
Unrelated to this term is the concept of a Virtual Private Number.