"Retainers" are NPCs that act as the storage system in Final Fantasy XIV: A Realm Reborn
Retainers are hardworking lads and lasses who will help you to manage those spoils earned while off slaying dragons or whatever it is you adventurers do.
You need to advance in the game in order to be able to hire a retainer.
You should be getting a Retainer Quest around levels 15-20
Otherwise they will tell you something like this:
"Unfortunately, you do not appear you could even slay an eft, let alone a dragon, therefore I must decline any petition you may have to take a retainer into your employ.
Build yourself a reputation in this city, however, and I shall provide you with whatever it is you need. Might I suggest you start by heading back to the Adventurers' Guild and seeing if someone there has work for you?"