The airponics bay was the garden Kes set up in a Voyager cargo hold in 2371, growing fruit and vegetables without soil to ease the strain on the ship's replicators.
The garden is proposed in Parallax, the second episode of the series. With replicator use rationed to save energy, Kes suggests growing fresh food in Cargo Bay 2 using airponics, in which the roots of plants hang in the air and are fed by a nutrient mist. Janeway approves at once.
The bay supplies Neelix's galley with produce, some of it from seeds and cuttings gathered on planets along the way. Kes tends it between her medical studies, and it is a quiet refuge for her in early episodes.
The garden is seldom seen after the Borg alcoves take over much of the cargo bay.