PBX refers to private branch exchange, primarily used in business telephone systems to have multi line support for multiple members of staff.
A PBX system is a business telephone system that will allow any phone in your company to be connected to the same network, be it physically in the office or remotely at a separate location. This type of system will allow you to have specific number dial through to multiple staff members and allow you to transfer calls between any members of staff on the system (usually for free).