Examples that come to mind are Schrödinger's Cat, the "inflating balloon" illustration of inflation or Hubble expansion, and the Bohr model of the atom (disproven as a viable model but still taught). These heuristic devices, in contrast to the Drake equation, are used to relate abstract mathematical concepts to more easily understood physical examples. That is their most important use, IMHO, but they carry the danger that people become beguiled by--and base objections on--irrelevant details of the illustrations, rather than grasp their salient points. (What if someone hears the cat meow? What is the balloon expanding into, and what if you're inside the balloon? Why aren't atoms flat like the solar system? etc.)
Some of the more far-out people in my area (rhetoric of science) tend to view all scientific expressions and equations as "giving names to things we don't know."
I don't think that's tenable. Consider the equation for rest mass energy, E=mc²: energy (E) is what we measure with a calorimeter, the speed of light (c) is what we measure with rulers and clocks; mass (m) is the ratio of force (measured by springs, for example) to acceleration (measured by clocks and rulers). All of these things are already independently known, or at least named unambiguously. Given these quantities, relation E=mc² is testably either right or wrong.