The part of a flowering plant that develops into a seed is the ovule.
When pollen grains land on the stigma of the correct species, they germinate. A pollen tube grows through the tissues of the flower until it reaches an ovule inside the ovary.
The nucleus of the pollen grain (male gamete) then passes along the pollen tube and joins with the nucleus of the ovule (the female gamete). This process is called fertilization.
After fertilization, the female parts of the flower develop into a fruit. The ovules become seeds and the ovary wall becomes the rest of the fruit.