The idea is that a single network is cheaper, easier, and more efficient to operate than multiple networks. Ideally a multiservice network is able to run applications of differing performance characteristics with a minimum of compromises. For example, voice requires minimal bandwidth, but is highly delay-sensitive.
File transfers require large amounts of bandwidth, but are relatively delay-insensitive.
Said another way, a multiservice network provides the ability to integrate all of your applications into a single network, with minimal performance compromises. The idea is that a single network is cheaper, easier, and more efficient to operate than multiple networks. But we'll get to that. The problem is that we get stuck on the golden-bullet idea. People get caught up in a particular technology and rely on that favorite to the exclusion of nearly everything else.