imagine a large WAN pipe going to a hosted pbx provider. they provide all the support like a hosted server (exchange, citrix, etc). if you have a problem, you call the NOC of the company that hosts your pbx. some allow you to make changes to the programing on your own, some don't. you can have them host all of the other servers (CAS, CDR, call recording) if they do that.
you have web interfaces or applications that connect to the PBX and other servers to pull reports and/or add & change configs.
the larger and cheaper the data pipes get, the more you'll see hosted solutions. i've come to the realization that in 5 years or less, my current employer will go with a hosted solution. they are getting the exchange, 4 x citrix, and other application servers hosted in 4 weeks.