This is a tricky topic because of the weird ways it appears in Lua.

Tuples are basically sequences of values not bound into a table.

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Tuples in Assignment

Here is the simplest use of tuples:

a, b = 1, 2
print(a) -- 1
print(b) -- 2

In assignment, a tuple (values separated by commas) are assigned to the respective variables at the left.

Tuples in Return

This also applies to functions which return multiple values:

function two()
	return 1, 2
end

a, b = two()
print(a) -- 1
print(b) -- 2

Or, for that matter,

print( two() )
-- 1	2

A warning; if you do any math to the values, you will lose all but the first:

a, b = two() * 3
print(a) -- 3
print(b) -- nil

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Passing Tuples to Functions

You can also use tuples as function arguments:

print(two())
-- 1	2

function sum(a,b)
	return a + b
end

print( sum(two()) -- 3

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Making Tables with Tuples

You can also use tuples with tables:

t = {3, two()}
print( table.concat(t, "\t") )
-- 3	1	2

A warning: if you put something after the value, you'll "cover up" the previous ones:

t = {3, two(), 4}
print( table.concat(t, "\t") )
-- 3	1	4

...Though if there were more it would continue:

function three()
	return 5, 6, 7
end
t = {3, three(), 4}
-- 3	5	4

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Unpack

Finally, there are the two ways to deal with this in general.

You can use unpack(tab) to turn a list tab into a tuple, e.g.,

five, seven = unpack( {5, 7} )

Varargs (...)

Or, you can use ... as the function parameter to get the list of things coming in:

function things( ... )
	local list = {...}
	-- Fills `list` with parameters (just like tuples in the previous examples)
	local sum = 0
	for i = 1, #list do
		sum = sum + list[i]
	end
	return sum
end

print( things( 5, 1, 2) ) -- 8
print( things( 1, 2, 3, 4, 5, unpack( {1, 2} ) ) )
-- sums 1 + 2 + 3 + 4 + 5 + 1 + 2 = 
-- 18

This lets you make variadic functions -- functions which can use any number of arguments, without you deciding the exact number ahead of time.

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Anything you want me to expand on or detail further, let me know and I'll add to this answer.