A Local is a stored or storeable variable input. It may be used to "hold" or store specific integers, reals, units, booleans and so on for later use in a function.
Locals are amongst the most commonly used variable storage agents in both JASS and vJass, as their versatility is widely appreciated and may even be titled as one of the most reliable executives.
Example of Usage:
function UsageExample takes nothing returns nothing local ResponsibleUnit = GetTriggerUnit endfunction
The above function uses the local storage agent to store a specific unit which has triggered the function, whether it be entering a region, casting an ability or so on.