The Flying Fish is a flying Enemy that spawns during rain. It follows a path much like the Eater of Souls, but has relatively low movement speed. Unlike most other flying enemies, it is able to freely enter water. Flying Fish will ignore players not in their line of sight, e.g. behind a wall or under a roof.
A Flying Fish in real life actually glides over water, instead of flying like it does in Terraria.
The Bestiary entry for the Flying Fish: "Certain species of fish gain the most peculiar abilities when it rains. They only like one thing about land-dwellers: their flesh."