What it's for - The moss is used in three recipies: Remedy (removes status ailments), Strength Potion (Boosts Strength 10-50% for 5 minutes), and Pet Roborant (removes a Beastmaster's pet's status ailment).
The most popular use - Raise Fame/Reputation in five cities at once: Bastok, San d'Oria, Selbina, Rabao, and Jeuno. This can be done by completing the repeatable quest "Only the Best" in Selbina. Each moss gives a 600 Gil reward. According to the comments on ffxiah.com, trading 25 stacks will give maximum fame. A stack price of 7,200 Gil will be break-even. Lower stack prices will be profitable. It is a very affordable way to raise Fame.