Staring — an open-eyed look of interest or amazement — is most often used as a verb but can also be an adjective. The man asked what you were staring at and his staring eyes seemed to look right through you.
The word staring comes from the root word stare, a fixed gaze. Its early meaning was "to be rigid," or "to stiffen," and later became "to look fixedly at." Staring is often rude, unless the person you are staring at is putting on a performance. Staring at the sun is not a good idea, since it can damage your eyes. When an answer is "staring you in the face," it should be obvious.