Both "relevance" and "lever" trace to the Latin root "levare" meaning "to raise up." English speakers adopted a form of "levare" as the basis for the adjective "relevant," meaning "having something to do with the matter being considered." From "relevant" they later formed the noun "relevance." A connection in meaning between "relevance" and "raising up" is not readily apparent. But "lever," meaning a bar that you can use to pry, raise, or move something with does maintain a clear connection. Other members of the "levare" family having to do with "raising up" include "elevate," "levator," which is a muscle that serves to raise a body part, and "leaven," which is a substance such as yeast that makes bread rise.