Honda started it, at least they released it first in the early 90's, on the NSX first, then the Integra GSR. They're the only ones I have any experience with so I'll give you what I know:
Two separate lobes on the cam, one for low RPM cruising, lower valve lift, better gas milage. Hit past 5500 RPM, switches to the other lobes, opening valves all the way, maximum output. Helps engine efficiency and gas milage if your not always hammering it, and can put more juice into it when you do. I think it adjusts timing, too, but not 100% sure on that. Seen those VTEC controllers? just allows adjustment of when the second lobes kick in, overriding factory setting of 5500 RPM.
Engines without it can do just as much HP if not more. I know plenty of Hondrossa racers around here that specifically search for non-VTEC engines to race.
Manufacturers use it mostly to keep their engines at ULEV standards and still show high peak HP numbers.