"run one on" means: To flirt with or make a pass at a woman, especially a woman already in a relationship.. This is informal slang, common in casual speech, texting and social media, but not appropriate for school work, applications or professional settings. There is no real cause for concern in itself; it is everyday peer vocabulary. If your child uses it, a light comment about audience and register is usually enough — no need to escalate. Context, more than the word, tells you whether to follow up.