Think first of a step-down DCDC converter. At its output, it consists of two switches (one to supply; one to ground) and an inductor.
When an inductor is carrying a current, it stores energy. When the supply switch is on, then current flows from the supply, through the switch, the inductor and into the load. During this time, the current in the inductor increases. Current (and power) is consumed from the input supply. Power is delivered the load, and energy stored in the inductor increases (because its current is increasing).
Now, when the supply switch opens, and the ground switch closes, the inductor current continues to flow; current flows 'up' from ground, through the inductor and into the load. During this time, the inductor current decreases.
Notice that during that 2nd period, current (energy) is still flowing into the load, and no power is being consumed from the input supply. The energy now being delivered into the load comes from the stored energy in the inductor.
If the switching frequency is high enough, the inductor current will look like a DC current with a triangular ripple superimposed on it. Generally a capacitor at the output will minimize the effects of this ripple component on the load.
Now you have a situation where current is only consumed from the power supply for a fraction of the cycle time, yet current is delivered continuously (with some minor ripple superimposed) to the load. This is the transformer-like behavior you mention.
An H-bridge is similar, with the motor's windings acting as the inductor.