A PBX (Private Branch Exchange) is a switch station for telephone systems. It consists mainly of several branches of telephone systems and it switches connections to and from them, thereby linking phone lines.
Companies use a PBX for connecting all their internal phones to an external line. This way, they can lease only one line and have many people using it, with each one having a phone at the desk with different number. The number is not in the same format as a phone number though, as it depends on the internal numbering. Inside a PBX, you only need to dial three-digit or four-digit numbers to make a call to another phone in the network. We often refer to this number as an extension.
This picture shows what a PBX does.
Read more on PBX: The functions of a PBX.