A groundless fear, rumour, or accusation is not based on facts or good reason. There is nothing solid under it. Ground here is not dirt; it is the older idea of a base or a reason, the same as grounds for a complaint. If a claim is groundless, you can ignore it, or you should stop worrying. The word is a little formal — you meet it in news, school essays, and careful speech more than in chat. Though actually, people sometimes say groundless when they only mean “I disagree,” which is looser than “there is no evidence.” It is the opposite of well-founded. Do not mix it up with grounded, which can mean “sensible,” “punished and not allowed out,” or “connected to the earth” in electricity.