They limit the scope of a variable.

x = 5

function apple()
    x = x + 5
    print(x)
end

function alternateUniverseApple()
    local x = x + 5
    print(x)
end

function banana()
    print(x)
end

If we do this, we get 10 and 10:

apple()
banana()

If we do this instead, we get 10 and 5:

alternateUniverseApple()
banana()

This is because the local version of x ceases to exist once you get outside of the scope. I believe that in Lua, scope extends to the edges of a function, but I might be wrong on that front.

Edit

As link has pointed out, what I've said about scope is incorrect.

In Lua, scope is to do with "blocks", rather than functions.

Consider the following:

function testFunction()
  local x = 5
  print(x)
  if x == 5 then
    local x = x + 5
    print(x)
  end
  print(x)
end

You get out 5, 10, 5, rather than the 5, 10, 10 you'd expect if scoping was to the edge of functions

Further information here

End edit

Why do you want this? Two good reasons:

• It allows the garbage collector to clean up variables you aren't using any more once they go out of scope, meaning your script uses less memory

• It means that you can reuse a variable name in one place without changing it in another

The idea of scope can be a little weird at first, so you probably want to have a little play around with it.