Here's why:
* It's formed by combining two words: "finger" and "tips".
* It functions as a single unit: It refers to the ends of the fingers, not individual fingers and tips.
* The meaning is different from the individual words: "Finger" refers to a digit, and "tips" usually refers to the ends of something, but "fingertips" specifically refers to the sensitive ends of fingers.
Therefore, "fingertips" meets the criteria of a compound noun.