The main task of the manifold is to distribute the plastic entering the mold to the various nozzles which then meter it precisely to the injection points in the cavities.
[1] Hot runner systems were first developed and came into sporadic use in the early 60s with generally negative results.
They gained popularity in the 80s and 90s as technological advancements allowed improved reliability and the escalation of plastic materials prices made hot runner systems more desirable and cost effective.
Hot runners are fairly complicated systems, they have to maintain the plastic material within them heated uniformly, while the rest of the injection mold is being cooled in order to solidify the product quickly.
Hot runners usually make the mold more expensive to manufacture and run, but generate savings by reducing non-productive plastic and allowing shorter cycle time.