The following is a paragraph from the International Plumbing code (http://publicecodes.cyberregs.com/icod/ipc/2009/icod_ipc_2009_9_par002.htm).
901.2 Trap seal protection. The plumbing system shall be provided with a system of vent piping that will permit the admission or emission of air so that the seal of any fixture trap shall not be subjected to a pneumatic pressure differential of more than 1 inch of water column (249 Pa).
In other words, the plumbing vent protects traps against atmospheric pressure differences that could cause them to siphon or blow out. I'm not sure what the plumber means by saying that the vent facilitates the flow of water from the roof… that’s what the gutter is for. Any water that enters the vent will drain into the soil stack but that’s a natural “side effect”, not a purpose.