When you set a function, what happens when you put something in the brackets?

The bracket for function() allows arguments to added in it. Example:

function(arg1)
    print(arg1)
end
arg1("Hello World!")

The function would print Hello World! This use can allow developers to quickly run codes without copy and pasting it. Also this is very important for modules scripts too.

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A more complex situation for this would be a script requiring a module script to summon a part Exmaple:

Module Script:

local module = {}
    function module:SpawnPart(position, partcolor)
        local part = Instance.new("Part")
        part.Position = position
        part.Color3 = partcolor
        print("Added part!")
    end
return module

Script:

local module = require(moduleScript)
module:SpawnPart(Vector3.new(0, 0, 0), Color3.fromRGB(0, 50, 100))

I would suggest searching up what arguments and parameters are because they play a major role in scripting. But I'll try to do my best to explain it.

--// Parameters are values inside of the brackets when you create the function

local function printingfunction(x)
    print(x)
end

--// Arguments are the syntax used when you call your function

printingfunction("Hello World!")

--> Console would print Hello World!

This is a simple example of arguments and parameters. You can create more complex functions with multiple parameters and arguments

Sources: http://wiki.roblox.com/index.php?title=Arguments_and_parameters