From Anime News Network:

The story is set 6,000 years after humanity has spread out across the stars, and takes place inside a gigantic city ship orbiting a remote gas giant. The ship is home to a civilization of space fishers that catch valuable fish-like creatures known as Besshu. The society harvests the Besshu through ships operated by enforced male-female pairs of operator and pilot, who are seen by the male-dominated society as a married couple. The story centers on Terra, who is seeking a partner to operate a ship, and finds her in the mysterious runaway girl Diode, with both uniquely able to use the ship despite both being female.