What is the difference between a function and a local function?

I've been wondering about this for a while now, and I couldn't find it on the wiki.

When I type:

local function h()
	print("HI!")
end

function a()
	print("HI!")
end

h()
wait(1)
a()

it prints HI! twice, as I expected.

But when do I use a local function and when do I use a normal function?

Thanks for your help!