~4.5 billion years ago, the proto-Earth (Gaia) was struck by a Mars-sized protoplanet named Theia. The collision released energy equivalent to billions of nuclear weapons, vaporizing much of both bodies and ejecting a massive debris disk into Earth orbit.
Within 1,000 years — cosmically instantaneous — gravitational accretion assembled this debris into the Moon. Evidence: the Moon's oxygen isotope ratios are nearly identical to Earth's (suggesting shared material), its low iron content implies it formed largely from the mantle, not the core, and its angular momentum matches the impact model precisely.
Recent refinements: Canup (2012) proposed a high-energy, high-angular-momentum variant where both bodies were similar in size, explaining the isotopic near-identity. The Moon was initially ~3× closer, receding to its current distance over billions of years via tidal friction.