The primary function of the ovary in a flower's gynoecium is to develop into a fruit.

The gynoecium is the female reproductive part of a flower, consisting of one or more carpels. Each carpel consists of three major parts - the stigma, style, and ovary. The stigma is the sticky surface at the top of the carpel that receives pollen, the style is a slender tube connecting the stigma to the ovary, and the ovary is the enlarged basal portion that contains the ovules.

The ovary plays a crucial role in the reproduction of flowering plants. It is responsible for the development and maturation of the ovules, which are the structures that contain the female gametes or eggs. After pollination occurs, the pollen grains land on the stigma and germinate, forming pollen tubes that grow down through the style and into the ovary. The ovules are then fertilized by the male gametes contained within the pollen tubes, resulting in the formation of seeds.

Once fertilization occurs, the ovary begins to develop into a fruit. The ovary wall thickens and undergoes various changes, such as the formation of additional tissues, to protect and nourish the developing seeds. The ovary may also undergo changes in color, texture, and size, depending on the specific type of fruit. This process is known as fruit development or fruit ripening.

The fruit serves several important functions for the plant. Firstly, it protects the seeds from external damage and provides a suitable environment for their development. It also aids in seed dispersal by attracting animals or wind, which help to spread the seeds away from the parent plant. Additionally, the fruit may contain substances that attract animals to consume it, thereby facilitating seed dispersal through their excretion.

In conclusion, the primary function of the ovary in a flower's gynoecium is to develop into a fruit. This process ensures the protection, development, and dispersal of the seeds, contributing to the reproductive success of flowering plants.