Find and Compare Bike Pedals for your Cycling
One description of the technique sums it up quite well: "pedal in circles". The essence of this is to use as much leverage as you can on the crank as it rotates, not just on the downstroke with each leg.
So for instance pushing down at the very top of the stroke or pulling up at the very bottom doesn't have much effect. On the other hand pushing forwards at the top of the stroke and pulling backwards at the bottom applies much more leverage to the crank and therefore applies more power, more efficiently, for a longer period.
Using clipless pedals which attach your shoe firmly, allows you to use this cycling technique and also brings other muscles into play to give you more power. Pushing with your knee towards the handlebars at the top of the stroke uses your inner quads, while pulling back at the bottom of the pedal stroke uses your hamstrings.
It takes a bit of getting used to and it is often useful to practice with one leg at a time, because that will reveal quite dramatically whether you are using the right technique or not. An obvious place to practice it when you are sitting on your bike on a turbo trainer !