Why does my output keep saying "Attempt to call a nil value" for my script ?!?!?!

Well, you actually need to define the function before calling it. For example, if I tried to do this:

eatFood("apple")

function eatFood(food)
    print("I just ate " .. food)
end

That errors:

ServerScriptService.Script:1: attempt to call global 'eatFood' (a nil value)

18:34:10.778 - Stack Begin

18:34:10.778 - Script 'ServerScriptService.Script', Line 1

18:34:10.779 - Stack End

It doesn't actually recognize the function eatFood because it hasn't been defined yet. Scripts are read from top to bottom, so if I want to call a function I need to make sure it already has been defined. Same goes for variables. If I do this:

print(variable)
local variable = "Hi"

That will give me an error, and it won't print. The reason it errors 'Attempt to call a nil value' is because the function hasn't been defined yet, and so to Lua doesn't recognize what you're trying to do. It then defines the function as a nil value. Here's your script fixed:

local play = script.Parent
local Frame = game.StarterGui.Check.Frame
local Check = game.StarterGui.Check


function onClick()
    Check.Frame.Visible = false
end

local Click = play.MouseButton1Down:connect(onClick)

Hope I helped, and if I did be sure to let me know and accept my answer :)

You're defining a function, in a variable, so that's why it is causing an error.

These are your new variables there was really no need to define click as it did nothing anyway.

local play = script.Parent
local Frame = game.StarterGui.Check.Frame
local Check = game.StarterGui.Check

This is your function, this just runs whenever a certain requirement is met.

function clicked(onClick)
    Check.Frame.Visible = false -- Makes the frame invisible.
end

This line of code just runs the above function, clicked, whenever the mouse is pressed down on play.

script.Parent.MouseButton1Down:Connect(clicked)

Here's the full code;

local play = script.Parent
local Frame = game.StarterGui.Check.Frame
local Check = game.StarterGui.Check

function clicked(onClick)
    Check.Frame.Visible = false -- Makes the frame invisible.
end

script.Parent.MouseButton1Down:Connect(clicked)

Note: From now on, you should get into the habit of using :Connect as :connect has since been deprecated.

If I helped, let me know! And don't forget to accept my answer, or if you need further assistance, leave a comment!