What purpose are coroutines used for? What are some examples in which coroutines are use in game?

I have been trying to learn the basics of coroutines, and I think they are used for multithreading. The thing is that I don't understand why they are used, can someone give me an example of how they can be used in-game on anything?

You are somewhat correct in that they are used for multithreading. Although they shouldn't be considered "true" multithreading.

You could for instance use them in an animation cycle, while performing some other task.

local part = game.Workspace.Part

local EndFlag = 0

coroutine.wrap(function()
	while EndFlag < 1000 do
		part.CFrame = part.CFrame*CFrame.new(0,.1,0)
		wait()
	end
end)()

--somewhere else in the script, perhaps in a function or some other logic

while EndFlag < 1000 do
	--Potentially some other simultaneous animation
	EndFlag = EndFlag + 10
	wait()
end

Is this efficient? No not at all. I don't even recommend using this method, however I hope this gives you an idea of some of the potential use cases.