Your correct S stands for Series i.e. 6s = 6 x 3.7v cells in series = 22.2v.
When deciding upon a setup for each size of heli your limited to available ESC's and li-po pack sizes/capacities.
Most people like a low current setups so go for as higher voltage as is available i.e. 6s for a 450 size heli which will barely average 15 amps.
Another example is you COULD run a 600 heli on 6s but again your going to need a much bigger ESC, wiring, connectors AND unless you run a 6s 6000mah+ single pack (which are hard to come by) you would need to run 2 packs of 3000-4000mah each ANYWAY.
So if you have to run 2 packs in a heli due to the limited capacities available why not run them in series and get a little extra power.
Remember you need to exchange voltage for capacity or visa versa to keep the weight down, you can simply add more Mah to get more flight time but your going to add extra weight.
60% of the time, it works every time!