Voice Over Internet Protocol, or in more common terms phone service over the Internet. If you have a reasonable quality Internet connection you can get phone service delivered through your Internet connection instead of from your local phone company. - http://www.voip-info.org/wiki/view/What+is+VOIP
PBX stands for Private Branch Exchange, which is a private telephone network used within a company or organization. The users of the PBX phone system can communicate within their company or organization and the outside world, using different communication channels like Voice over IP, ISDN or analog. A PBX also allows you to have more phones than physical phone lines (PTSN) and allows free calls between users. It also provides features like transfers, voicemail, call recording, interactive voice menus (IVRs) and ACD call queues.
PBX phone systems are available as Hosted or Virtual solutions (sometimes also called Centrix), and as inhouse solutions to be used on your own hardware.
PBX phone systems are usually much more flexible than proprietary systems, as they are using open standards and interfaces. Modern PBX phone systems are based on standard hardware, which is cheaper and can easier be replaced than a closed systems.
Hosted PBX is a service where the call platform and PBX features are hosted at the service provider location. The business end users connect via IP to the provider for voice service.
Unlike a traditional PBX, or Private Branch Exchange, which requires a large investment and ongoing maintenance and training, a hosted PBX is a cloud-based PBX system accessible via an IP network. Rather than being responsible for hardware, software, training, maintenance, and more, a hosted PBX provider takes care of it all. In addition to being completely managed off-site, resulting in no IT or installation costs, a hosted PBX system also provides businesses with the ability to manage their phone systems via a user-friendly control panel. For these reasons and more, hosted PBX systems are becoming increasingly popular solutions for today’s growing small to medium-sized business owners.