Well, VVT is a technique in which the time the intake valves stay open is controlled by other means in addition to that based on the engine's RPM. In a non-VVT engine, as the RPM increases, the time the valve stays open also becomes less (so in a way the open time is variable with RPM but opens and closes at a faster rate) and as a result the engine is not as effective at sucking in air - but with VVT a valve may be made to stay open longer with increasing RPM. The overall effect is that the engine can breathe better and along with fuel injection can give better performance/mileage. VVT is achieved by having more than one cam profile per valve and selecting a cam based on the RPM range.
To see the benefits...
A non-VVT engine will suck air based solely on the RPM - the amount of air may be too much or too little for the RPM and the only way the ECU can ensure adequate efficiency is by controlling the amount of fuel injected. For example at low RPM the intake valves will also stay open longer - so chances are that more air than needed is getting sucked in - and the ECU will inject enough fuel to match that air using the ideal air-fuel ratio. So we can see that more fuel is being burnt - so less mileage.
In a VVT engine, there could be 2 or more cam profiles for different RPM ranges (or load conditions), such that at the lowest range (or load condition) the cam profile chosen will be the one that ensure minimum air required to maintain the RPM. The ECU will still inject fuel based on the amount of air sucked but this time the amount of fuel will be less as compared to the non-VVT engine. Hence we can see that the engine will burn lesser fuel and hence give better mileage.
 S = k.I^2, where S is the amount of stupidity a species possesses, I is the intelligence the species has and k is the universal constant of stupidity.
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