A fly is a specific type of insect with wings. They are known as pests, and can sometimes carry disease.
When Sito Jaxa suggested that it would be good to be a spider under the table of the observation lounge, Sam Lavelle compared this to be a fly on the wall. They were talking about the meeting of the senior staff in the observation lounge and were curious what they were talking about. (TNG: "Lower Decks")
Roy was a holographic fly created by Doctor Lewis Zimmerman in the 2370s for Starfleet Intelligence as a new form of micro-surveillance on the "Trojan Horse Project". When his mission was complete, Dr. Zimmerman kept him around on Jupiter Station as a pet. He nonetheless often landed on The Doctor's food. (VOY: "Life Line")