What is the Break Variable?

break is not a variable, it is a 'keyword', which is why it is colored blue in the script editor.

break is used to, as the name implies, break out of a loop before its condition would otherwise allow.

For example:

local var = 0
while var < 20 do
    var = var + 1
    wait()
end

and

local var = 0
while true do
    var = var + 1
    if var >= 20 then
        break
    end
end

are functionally identical.

A practical use of break is quitting a Murder-type game's loop when the Murderer is killed or otherwise leaves the game.