Convergence is the phenomenon of voice, video and other forms of data coming together on the same network rather than having separate cabling. A shared network has some inherent issues (such as the potential for data loss and delay) but it is the development of effective solutions to these issues that has enabled and driven convergence.
Voice traffic is sensitive to packet loss and latency so on a busy network steps need to be taken to ensure audio quality. QOS (quality of service) is a mechanism that allows the network to prioritise voice and video data over other data, preserving call quality.
Not only do shared networks save on cabling, they have distinct operational advantages. The development of standard protocols such as SIP enables system components from different manufacturers to work effectively together and IP systems make it easier and cheaper to build-in resilience, for example using fail-over servers.