A lighter is one of the most useful things invented (and not just for lighting fires) as it lets you suss out what's real and what's not. Basically, if it melts or burns- it's geneally a synthetic. But if it singes, it's not.
Lets look at silk & cotton vs. poly/nylon ect ect. Silk and cotton, when exposed to a naked flame, will always singe and won't really catch alight. The ends will still look a bit... "tatty." Whereas if you expose a synthetic fibre to a naked flame, it will bubble and boil and burn for a few seconds. The ends where you burnt will almost be fused together. Unless it's been flame treated (unlikely) you will notice a synthetic fibre will burn better (alot better- a couple of seconds more then a cotton or silk) then a natural fibre. Not only that, but if you are wearing natural fibres and your clothes happen to catch on fire, they will merely burn and turn to ash- while synthetic fibres will melt to your skin. This is espically important when you are buying sleepwear for children.
Another thing is, silks feel more natural. I can nearly always tell the difference between silk and polyester simply by touch- poly doesn't seem as "dry" as silk and feel more oiley.
The same method works on leather too, except instead of burning a corner of the fabric, you hold the lighter underneath for a few seconds.