The Whale is a creature that can be seen in Sector Y.
In the comics
In the Nintendo Power comic, the whale's backstory is explained. It is a "transdimensional manifestation of a starship" which had rescued Fox McCloud, Senior from the Black Hole, and thenceforth he helped them understand the primary universe. When the Star Fox team liberates the Stingrays from their controlling antennas, the whale appears through the black hole's warp field to save the Lylat System and leaves fuel canisters for the team's Arwings. Then Fox Sr. informed the team that Andross was to be found on Fortuna.
Fox Sr. became a part of the crew of the Whale when his Arwing was caught in the Black Hole and "warped to another dimension". This could be a reference to the secret Out of This Dimension stage which could possibly be the permanent residence of Fox's father, as he says he's "A part of this dimension" and that he "can't cross back", most likely referring to how escape from Out of This Dimension is impossible.