Look like I am late to party. Everybody given the definition and quoting the source so I am not going to repeat the same definition.

Lets go in definition of word "Avalanche".  Actually avalanche is a snow slide or in other words a large mass of snow going down by the violent force (due to gravity). It is very dangerous and can have speed of 80 miles per hour or 128 km per hour. They just need a trigger  that is most of time is provided by human activity. Actually snow in steep slope are in a delicate balance and if this balance is broken then gravity start playing its role. They can grow more strong in their downward journey gathering more snow and disturbing other delicate balances too.

So slight change in input (trigger) causing the output to change too much (disturbed balance) is Avalanche effect.

Hope you guys enjoy this relationship between a natural effect with a cryptography phenomenon.