What precisely does the "potency" of an opioid measure (i.e. levorphanol is seven times more potent than oral morphine) ?

Potency: The amount of drug required to produce the same effect.

Relative strength : Potency refers to the narcotics relative strength when compared to a set standard. The drugs ability to control pain when compared to a standardized medication such as morphine. This is assuming we are using the same administration route (oral vs. intravenous).