What does this character do?
In the broad sense, aristocrats provide rulership, refinement, and culture to everyone not among the aristocracy. Especially the way that they tell it. In more practical terms, aristocrats lounge and mince about while everyone else does all of the hard work. These are people whose lives are defined by having far more money and power than they need or could even want, the people who have never wanted for anything if it wasn't one of a kind.
Obviously many player character aristocrats will have some restrictions placed on their in-character wealth to explain why they can't simply buy their way through everything, but the important part is a lack of want. Even if he no longer has a penny to his name, an aristocrat is accustomed to having much of his life taken care of by other people, and he need only concern himself with the highest levels of his day-to-day activities. There's no need for him to worry about having clothes to wear or places to sleep or meals to eat. All he has to do is wear what he's given, and events will naturally fall into place.
This does not mean that the aristocrat is useless, although he certainly might be. But having all the time in the world to pursue literally anything you want can sometimes lead to frighteningly capable individuals. That capability may very well be in narrow and only occasionally useful fields, but even the most useless aristocrat has at least been forced to get good at socializing and schmoozing.
What does this profession provide for roleplaying?
Depending on the setting, sometimes just having an aristocrat in a group can make a big difference. Sponsorship from Ul'dahn aristocracy in Final Fantasy XIV is a big deal, and being the favored minion of a Sith Lord in Star Wars: The Old Republic carries plenty of weight. In some settings, nobility isn't really worth menioning, but with the aristocrat, you may find doors opened in-character that should otherwise be closed.
From a backstory perspective, aristocrats can serve another function: They can give your character access to ridiculous skillsets that make no sense. Aristocrats universally have time to spend learning all sorts of crazy things, so if you really want your character to be a linguist and a professional fencer, he could conceivably learn and practice both during the time that everyone else was learning how to avoid getting eaten by a wolf. There's no reason your character has to be ineffectual unless you want him to be.
What sort of characters work best in this role?
Aristocrats in fiction generally come in one of two flavors. You've got the self-congratulating bastard who spends so much time looking down on people that you'd swear he was wearing stilts. Then you've got the ideal noble who cuts an inspiring figure and lives up to all of the ideals that are tied to nobility, perhaps unfairly.
The reality is that since aristocracy is generally an inherited position rather than an earned one, almost anyone can wind up with a silver spoon in his mouth. A successful noble is probably at least moderately happy talking with others and earning the respect of those around him, but there's nothing saying that your aristocrat has to be any good at it.
As a result, unlike characters in professions that reward a certain sort of mentality, the characters best suited to being aristocrats are the ones who do something interesting with the concept. Imagine a Paladin, for example, who fully believes in his own inherent nobility... and is still self-sacrificing, generous, and virtuous. He never rants at you about why you're wrong, but he's still subtly patronizing, and it winds up creating a very different dynamic: His behavior actually lends some credence to his arguments.
What should I keep in mind?
While there are a lot of people who can potentially be adventuring as aristocrats, one thing that's universal is that aristocrats are accustomed to having power. Your character might be running from his aristocratic heritage, but he's still used to people listening to what he has to say, no matter the environment. This can either lead to the character's getting rudely introduced to a world that does not care, or it can be a call for the aristocrat to find more authoritative ways to call the attention of others.
You know, like guns.
Also worth noting is that aristocrats don't generally live in an environment conducive to genuine feedback. This isn't to say that they expect everyone to love them unconditionally, although some will. Most aristocrats are a bit more convinced that they're right than is entirely healthy, just the same, so feel free to have even a more humble character march headlong into something everyone warns him about.
Feedback is welcome down below or by mail to firstname.lastname@example.org, as always. Next week I'm going to look at roleplaying within a beta environment -- whether it's worth it, what you can do, and how it can actually hurt your long-term enjoyment.
Every Friday, Eliot Lefebvre fills a column up with excellent advice on investing money, writing award-winning novels, and being elected to public office. Then he removes all of that, and you're left with Storyboard, which focuses on roleplaying in MMOs. It won't help you get elected, but it will help you pretend you did.