Suppose $S$ and $T$ are consistent recursive extensions of $\text{ZFC}$. Then $T$ interprets $S$ iff $T$ proves each $\Pi_1$ consequence of $S$.
Set theorists use this to gauge the consistency strength of "natural" extensions of $\text{ZFC}$, which are (as far as people can tell) prewellordered under the relation of interpretability. In other words, the natural extensions form a well ordered hierarchy of degrees of interpretability. This is amazing, since it's easy to construct natural extensions that seem to have nothing in common—say, $\text{ZFC + }$"projective determinacy" and $\text{ZFC + }$"a supercompact cardinal exists."