Pig Island was found by Honeydew in Part 5: The Legend of Pig Island and was named simply because it was a floating island with a tendency to spawn pigs. It is located not far from the Yogcave. It is where Honeydew and Xephos got their first porkchops. They returned to Pig Island in Part 18, but only explored the cave below it. It's where Xephos and Honeydew got reunited when they were lost.
Pig Island is also known as 'The Magical Island of Pig'.