TDM, phone technology based on circuits switched by venerable PBXs, provided valuable services for a long time. Everybody got their own extension, a fancy corporate phone, voice mail and sometimes extra features such as conferencing, multiple call appearances and caller ID.
It was reliably maintained by well-trained telecom staffers who knew their switches like the backs of their hands.
When VoIP came along, promising to run voice calls over IP networks for less money, customers were intrigued. Rather than send out a technician to move a phone extension from one office to another, the user just had to move their phone to a new jack and it would receive calls meant for the person it was assigned to, no technician required.
Rather than supporting two separate networks, VoIP riding on the data network would allow them to get by with one. If voice was just an application running on the network, the telecom staff wouldn't be necessary or at least wouldn't need to be so large.
The cost savings proved to be a red herring, but in the cases where business adapted VoIP, they found other reasons to like the technology. If a customer help line in one office was swamped, more agents from anywhere on the network could quickly and painlessly be routed into the call-distribution list and start fielding calls.
VoIP supports services TDM doesn't, such as popping up account information about customers on call agents' computer screens based on the caller IDs or enabling users to place calls by clicking on phone numbers within applications or finding out who is available to take a call transfer by using presence information that VoIP supports.