Charged leptons are a breed of elementary particle that comes in three masses: the lightweight electron, responsible for the electricity in our homes; the middle-weight muon; and the heavy tau. Two other types of elementary particles, quarks and neutrinos, come in three masses as well.
You might not think about dogs while you wonder about particle physics, but there are similarities. Poodles, for example, also come in three sizes—toy, miniature and standard—but they're all the same breed, and genetically similar. Learning how poodles and other breeds are related helps us understand the rules of dog genetics.
We want the same type of understanding of how elementary particles relate to one another. Quarks can change from one type to another; so can neutrinos. If you want to have any sensible “laws of genetics” for particle physics, that last breed, the charged leptons, had better be able to change types as well. That's called charged lepton flavor violation. Surprisingly, physicists have never seen it happen.
Previous experiments have looked at about 10 trillion muons; Fermilab's Mu2e experiment will observe 10,000 times more data, looking for a change from a muon to an electron. Discovering this change would point us toward a single theory explaining the genetics of the particles born in the big bang. If we don't discover this change, there will be a lot of head-scratching (as opposed to fur-scratching) as we try to understand the rules of the universe.