What's the difference between a local variable and a variable?

I'm going to preface this by saying that I don't wan't any code, but rather to further my understanding about scripting.

I've been scripting for about 2 years now, and I'm starting to get serious about it. And one question that I've been asking myself is what is the difference between a local variable and a regular variable.

Regular Variables

function removeItem()
	player.Backpack.Item:Destroy()

end




while true do
	wait(3)
	
	players = game.Players:GetChildren()
	
	player = players[math.random(1,#players)]
	
	removeItem()
	
	
end

Local Variables

function removeItem()
	player.Backpack.Item:Destroy()

end




while true do
	wait(3)
	
	local players = game.Players:GetChildren()
	
	local player = players[math.random(1,#players)]
	
	removeItem()
	
	
end

This script works perfectly, but when I defined everything as a local variable it didn't work, and I was getting errors everywhere. Why does this work now?