What are all the generic loop functions?

I would really like to know, right now all I can understand is the index function. Would someone mind explaining the rest?

pairs, ipairs and next are the built-in global functions used in generic for loops for indexing through tables. I don't know anything about an "index" function.

local t={'a','b','c','d','e','f',a=1,b=2,c=4,d=8,e=16,f=32}
for _,v in pairs(t)do
	print(_,v)
end

Output:

1	a
2	b
3	c
4	d
5	e
6	f
d	8
e	16
f	32
a	1
b	2
c	4

pairs has no particular order for indices that are non-numerical.

for _,v in ipairs(t)do
	print(_,v)
end

Output:

1	a
2	b
3	c
4	d
5	e
6	f

ipairs does not index non-numerical indices at all.

for _,v in next,t do
	print(_,v)
end

Output:

(same output as pairs)

Calling next(t) will tell you whether or not the table is empty.

The generic for loop can also be used with your own functions:

for v in function(_,n)
	return(n or 0)+1
end do
	print(v)
end

This will count up forever.

While true do -- Infinite Loop, crashes if there is no wait()
print("hi")
wait(1)
end

for i = 1,10 do --For loop. This loop will print yo 10 times. 
print("yo")
end