The term “hosted VoIP” has both broad and narrow definitions. In the broadest sense, the term could apply to any type of VoIP phone service, from residential to business-class. In the business environment, a hosted VoIP service could be provided by a third party (externally hosted), or “hosted” on servers inside the company using it (on premise PBX).
Typically, however, hosted VoIP means a Voice over IP (VoIP) service for businesses that is provided by an outside company. The hosting is usually done in colocation (multiple companies using one facility) data centers. People using these services should make sure that the data centers have sufficient power, connectivity, and redundancy to provide high availability.
Hosted VoIP phone services for businesses usually include both the ability to make and receive calls over the internet and the ancillary telephony services that are needed for business use, such as voicemail, call routing, virtual attendant, etc. Administration for VoIP business phone systems is usually provided through web browsers.