Power dissipated or generated through an element
One way to define voltage (electrostatic potential) is the answer to the question "how much energy would it take to put an element of charge at this location?".

So if charge enters a circuit element with a certain amount of energy, and leaves with less energy, the energy of the charge must have gone somewhere in the element.

On the other hand, if charge enters a circuit element with a certain amount of energy, and leaves the element with more energy, the element must have done something to increase the energy of the charged particles involved.