From Brotato Wiki
Snake makes any burn you inflict be able to spread its debuff to any nearby enemy that isn't already burning. Each snake increases the amount of times the burning effect can spread by +1.
The spread can happen at any point during the burning duration. Fire spread by snakes can also spread to more enemies, but it uses same counter, so if you have 3 snakes, it can still only spread a total of 3 times, but any of the targets put on fire can spread it.
Snakes also makes Incendiary Turrets spread their fire to more targets.