Adjustable timing / lift / cam profiles. Basically once the engine is spinning past a certain number of revolutions / minute, it shifts into a mode that allows it to make better use of its fuel and air at that higher speed.
Regular VTEC will either be engaged or not engaged, while i-VTEC is a variable system - it can be working 'a little' or 'a lot' depending on how fast the engine is running. Honda has VTEC systems in use to increase performance as well as improve fuel economy. Other manufacturers use similar systems to achieve similar results.
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