Trance Gemini is the de facto gardener of the plants, as she has an affinity for all living things. Her relationship with the plants that she grows is strong, as she gives them names.
It is the main source of fresh food and oxygen for the ship, and is also a place for crewmembers to relax and play games such as Basketball. The garden is a massive area that sprawls over several decks, and has a very large unidentified tree at the center of the area. It has at least 3 entrances, which are equidistant from each other and are very large, more akin to the interior doors leading to the cargo bays than other, smaller interior doors. ("D Minus Zero", "Under the Night", "Pitiless as the Sun")
The Hydroponics bay is most likely located slightly forward towards the center of the ship, for several reasons. They Hydroponics bay is very important to both the life support systems on the Andromeda as well as to the food processing systems, which in turn helps crew moral. Because of its importance both in the minds of the crew and the technical importance, it has a large space on board the Andromeda. It is probably located in the center of the ship because the ships hull and corridors can be built so that they go around the bay while at the same time allow for structural reinforcement. Being located at the center of the ship also gives it passive defensive protection: any kind of damage that would be done to the garden by either invading troops or a hull breach would be almost impossible, as external doors could be closed to protect it before any hostiles reached it. And, any explosion of damage severe enough to extend and influence the state of the garden would likely be so great that the entire ship itself would be lost. The loss of the Garden due to anything, be it a firefight or catastrophic collision, would hit the ship very hard although it would not be a critical loss. The garden, while helping to purify and refresh the air while simultaneously providing supplements to the ships diet does not serve an irreplaceable role. The Andromeda Ascendant could her Nanobots to mine asteroids for oxygen and new water, as well as finding compounds that could be made converted into something edible, and the Ramscoop could also help to refresh the gases inside the ship. However, doing all of that harvesting mechanically would take valuable time, and require the Andromeda to stay in one place for a rather long period of time.
Hydroponics refers to the process of growing plants in a nutrient rich solution of oxygenated water, with no soil involved. It is suited to space travel, as the checmicals and nutrients needed to create a solution can be harvested from Asteroids and gas clouds. But, on the Andromeda, where space is not an issue and plants can be properly grown without the care and finesse needed to grow hydroponics, dirt is used. Some plants are grown in a Hydroponic solution, but many of the larger, established plants such as trees, flowers, and bushes are grown in dirt because of the stability and easy care that it involves.