Skilled and serious, or job, or both. To me some people look very professional while it's only their hobby. I don't want to call them hobbyists just because they don't earn money with it. They deserve to be called professional too!

very skilled at art~

Someone to take very serious his/her artistic skills so treat to draw as a job.
(sorry for bad english)

"Proffesional" does not necessarily mean that they're skilled, or good at giving a message through their art. In fact, the status of 'professional' is usually more about their connections than anything else. A professional can life off their skill alone: whatever they're a professional of, they can use that skill to support their lifestyle. That's all.

That means that the people that get their art into galleries aren't necessarily the best or most creative or what have you. Some guy just heard of them from a guy that he owes a favor to - or some other similar social contrivance. Does that mean skill means nothing? No, crap is crap, and no one will take it if it's that obvious you suck, but social skills are just as, and sometimes more-so, important. As is luck.

We call the people that show great skill/vision "Masters." This is true for any form of craft: The masters are the ones that are good, and the professionals are the one that live off their work. The doesn't mean you can't be a professional AND a master, and most crafts require mastery before you're taken seriously as a professional, but the two are not in the least exclusive.

Wiki: A professional is a person who is paid to undertake a specialised set of tasks and to complete them for a fee.

so I guess they make a living through art?

being a professional artist is when you can convey your thoughts and feelings through your art, and also having the love for what you do.

Also, you can be a professional without being paid guys. I'm a professional slacker but you don't see me getting an hourly wage Professional just implies you have a greater degree of skills and mastery really.

Someone who has reached reasonable satisfaction with their craft of choice, and uses it to enrich their own lives as well as the lives of others.

By definition, being a professional in anything means that you make a living off of whatever you're doing.

A pro artist is someone who can:

Express ideas
Understand the value of their own work, even when others dislike or hate the piece
Are able to enjoy their work even if it's not "perfect"
Share messages and thoughts on other artists work in a humble non-rude critique (You can be negative, just don't go "This is wrong, that's wrong, and you're anatomy sucks" but a pro will point out good and bad and offer suggestions with the other artist's ideas or intentions)
Humble about their work. Too much rubbing it in peoples faces makes you look like a kid. (AKA don't shove you're epic abilities in peoples faces)
Able to accept negative critique (This is why I don't really title myself as a true prof yet. It only says it because that is my only job. -.- But really I can't take some critiques....usually it's the ones like the above from people who are "you did this and this and this wrong")
Constantly improve
Find new styles even when they're comfortable in their own
Try something new (paper, ink, oil pastels) in media

And well that's all I can think of.