A facial expression was a form of non-verbal communication that could indicate an individual's emotions. It involved contorting one's facial muscles.
In 2366, Data surmised based on Natasha Yar's facial expression that she was considering something disagreeable. She corrected him, saying that she was merely preoccupied with many things, including wondering what would become of an USS Enterprise-C officer she was working with. (TNG: "Yesterday's Enterprise")
In 2371, despite being unable to read Odo's emotions, Lwaxana Troi guessed by the look on his face that something was bothering him and asked him to tell her. He denied it. (DS9: "Fascination")