From AMS Glossary
The process in which a relatively small number of free electrons in a gas that is subjected to a strong electric field accelerate, ionize gas atoms by collision, and thus form new electrons to undergo the same process in cumulative fashion.
All streamers in a lightning discharge propagate by formation of electron avalanches in the regions of high electric field strength that move ahead of their advancing tips. Particularly in the case of the intense return streamer, avalanche processes are enhanced by formation of photoelectrons as a result of ultraviolet radiation emitted by the excited molecules in the region just behind the tip. An avalanche cannot possibly begin until the local electric field strength is high enough to accelerate a free electron to the minimum ionizing speed in the space and time interval corresponding to one mean free path of the electron, for upon collision, the electron usually loses its forward motion in the direction of the field. Maintenance of an avalanche requires a large reservoir of charge, such as accumulates more or less periodically in active thunderstorms.