One example is thermal columns extending above the top of the equilibrium level (EL) in thunderstorms: unstable air rising from (or near) the surface normally stops rising at the EL (near the tropopause) and spreads out as an anvil cloud; but in the event of a strong updraft, unstable air is carried past the EL as an overshooting top or dome.
This overshoot is responsible for most of the turbulence experienced in the cruise phase of commercial air flights.
This affects the heat transfer rate and the temperature of the solar interior which can be indirectly measured by helioseismology.
The layer between the Sun's convective and radiative zone is called the tachocline.
As a result, the core mass at the end of the main sequence can be larger than would otherwise be expected.