What IS Direct dial ?
 

Local telephone companies offer a service to connect a customers' private branch exchange (PBX, responsible for switching the calls to the appropriate extension) system to the PSTN (Public Switched Telephone Network, or the traditional telephone network, which does not use the Internet during a phone call). It is called Direct Dial-In (DDI) or Direct Inward Dialing (DID numbers), both are explained in a later paragraph.

It is made on an external VoIP (Voice over Internet Protocol, a protocol, which defines the transmission of multimedia sessions via the Internet) phone, and gets transmitted to the PBX of your company, where it is switched to the desired local extension.
If an internal call is made, however, then the call is simply transmitted from a VoIP phone to the PBX, where it gets switched to the appropriate extension within the company. This process takes place entirely in the local network.