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What is avalanche capability?

Owing to the stray inductance of the circuit, the surge voltage of the MOSFET is superimposed on the voltage between drain and source at turn-off, and the drain-source voltage may break down if it exceeds the maximum rating of the device.
However, MOSFETs do not break even at voltage exceeding VDSS (rated voltage) when energy and drain current are within certain limits and temperature is under the rated channel temperature Tch. This is called avalanche capability. The allowable energy is called avalanche energy (EAS) and the current is called avalanche current (IAR).

Maximum Ratings: Power MOSFET Application Notes (PDF:1,075KB)

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