Turtles are Lost Animals who will occasionally wander on to your farm. Farmers have the option to help the animal or send it away. By helping it, it becomes available for a farmer's neighbors to adopt. A turtle takes 3 days to grow and farmers may collect eggs from them, which earns the farmer 86 coins. Interestingly, despite mentioning in the adoption notice that the turtle is male, you harvest its eggs. It is based off the real world turtle. The description may be based off of the Aesop's fable: "The Tortoise and the Hare", in which the Tortoise and Hare have a race.
For about 2 months the Turtle could not be found on a farm, but then came back with other lost animals!