lepton number
Lepton number is a simple bit of bookkeeping that nature seems to obey: in any reaction, the number of leptons minus the number of anti-leptons stays the same before and after. You can think of it like a ledger where every lepton counts as +1 and every anti-lepton (such as a positron or an antineutrino) counts as -1. Add up the entries before a reaction and after it, and the totals must match.
Take the classic example of a neutron decaying. A neutron turns into a proton, an electron, and an electron antineutrino. The proton is not a lepton, so it contributes 0. The electron is a lepton, +1. The antineutrino is an anti-lepton, -1. So the lepton total after the decay is +1 plus -1, which equals 0 — exactly the same as the 0 we started with (the neutron is not a lepton either). The antineutrino has to appear precisely so that the books balance.
Lepton number is what physicists call a conserved quantity — a tally that does not change, the same idea behind the conservation of electric charge. Conservation laws like this are powerful: they forbid huge numbers of reactions that would otherwise be allowed by energy alone, and they predicted that an unseen partner (the neutrino) had to be emitted in beta decay long before anyone caught one. Whether lepton number is truly exact, or only very nearly so, is one of the open questions tied to whether neutrinos are their own antiparticles.
When a muon decays, a muon (lepton, +1) becomes an electron (+1) plus a muon neutrino and an electron antineutrino: +1 from the electron and the muon neutrino is +2, minus 1 from the electron antineutrino gives +1 — the same as the single muon we started with.
The ledger balances at +1 throughout the muon's decay.
Lepton number is an observed rule, not a deep theorem of the Standard Model; a hypothetical process called neutrinoless double beta decay would violate it, and finding it would tell us neutrinos are their own antiparticles.