Trying to get an automatic weapon to work, but it will not fire?

Let's look through this code and understand what it's doing. I presume local variables automaticFire, mouseDown, tool, and fireRate are defined before the code you provided, as well as the fireBullet function.

tool.Equipped:Connect(function(mouse)
	print("Tool equipped!")

This is pretty simple. It connects a function to the Equipped event of the tool. It receives in a mouse parameter. Then it prints "Tool equipped!". Everything is working so far.

Now we have this:

mouse.Button1Down:Connect(function()
	if automaticFire then
		mouseDown = true
	else
		fireBullet()
	end
end)

So we take the mouse we were given, connect to its Button1Down event, and then do one of two things. If automaticFire is true, we set mouseDown to true, otherwise, we call the fireBullet function. So far so good.

Next is this:

mouse.Button1Up:Connect(function()
	if automaticFire then
		mouseDown = false
	end
end)

Here we connect to the mouse's Button1Up event a function that will reset mouseDown to false if automaticFire is true. Still working.

Finally, we have this:

	while mouseDown and automaticFire do
		fireBullet()
		wait(fireRate)
	end
end)

This would normally be fine. However, in this case, the conditions are checked once, when the tool activates, and since mouseDown isn't true to start with, it will skip the loop and never fire. Not what we want.

To fix this, we need to put this loop somewhere that will run every time we might fire. How about the Button1Down event connection?

mouse.Button1Down:Connect(function()
	if automaticFire then
		mouseDown = true
		while mouseDown and automaticFire do
			fireBullet()
			wait(fireRate)
		end
	else
		fireBullet()
	end
end)

Now since once we get to the loop, we know both mouseDown and automaticFire are true, it will enter the loop and continue firing.

Now there are two minor things we can change. First, in the loop, since we are in the if statement that checks if automaticFire is true, we don't have to check that in the loop. Second, if fireRate is given in rounds per minute or a similar measure (for example, 500 rpm), it will wait that number in seconds (500 seconds). Not exactly what we want. We can instead take the reciprocal of that number to get minutes per round, then multiply that by 60 to get seconds per round, which is how long we want to wait.

mouse.Button1Down:Connect(function()
	if automaticFire then
		mouseDown = true
		while mouseDown do
			fireBullet()
			wait(60/fireRate)
		end
	else
		fireBullet()
	end
end)

Note that there is a minimum wait time, so you may only be firing 30 rounds per minute instead of the number you expect.