Why Overmodulation drives the modulator past its linear range, so the audio is clipped and distorted. Clipping creates harmonics and intermodulation products of the audio signal, and those extra frequencies appear as additional sidebands far from the carrier. The result is splatter, interference to stations on adjacent frequencies, and occupied bandwidth much wider than the transmission needs.
Watch out Insufficient audio is the opposite condition, undermodulation, which just makes your signal weak and hard to copy; frequency drift comes from an unstable oscillator or thermal effects, not from audio level.
Too much modulation equals too much bandwidth: overdriving audio splatters onto the neighbors.