An artist's statement should be an explanation of your painting style and subjects or themes. Add a bit about your approach or philosophy if you wish. Mention your education, specifically if you've studied art (the closer you are to the date you left art college, the more relevant this is). Consider mentioning which artists (living and dead) have influenced or inspired you.
Mention any significant awards you have won, exhibitions you have participated in, collections your paintings appear in or significant sales you may have made, and painting organizations or societies you belong to. Remember, though, you're aiming to create professional credibility by highlighting your achievements, not providing a full resume.