The correct answer is option 'C', the outer integument.

A seed is the mature ovule of a plant that contains an embryonic plant, stored nutrients, and a protective seed coat. Seeds are formed through a process called seed development, which involves the fertilization of the ovule and the subsequent development of the seed coat and embryo.

Here is a detailed explanation of the development of a seed and how the outer integument plays a crucial role in this process:

1. Fertilization: The process of seed development begins with the fertilization of the ovule. Pollen grains from the male reproductive organ (stamen) are transferred to the female reproductive organ (pistil) of a flower. The pollen tube grows down through the style and reaches the ovule, where fertilization takes place. The male gametes (sperm cells) are released from the pollen grain and fuse with the female gametes (egg cells) inside the ovule.

2. Ovule development: After fertilization, the ovule undergoes transformation into a seed. The ovule consists of various layers, including the outer integument, inner integument, nucellus, and embryo sac. The outer integument is the outermost layer of the ovule, surrounding the inner integument and nucellus.

3. Seed coat formation: The outer integument, also known as the testa, plays a vital role in the development of the seed coat. It undergoes changes and differentiates into the hard, protective outer layer of the seed coat. The seed coat serves to protect the embryo and the stored nutrients inside the seed from mechanical damage, desiccation, and pathogens.

4. Embryo development: While the outer integument is developing into the seed coat, the embryo inside the ovule also undergoes development. The zygote, formed by the fusion of the male and female gametes, divides and differentiates into various tissues and organs of the embryo. These include the embryonic root, shoot, cotyledons (seed leaves), and the embryonic axis.

5. Maturation: As the embryo continues to develop, the surrounding tissues of the ovule, including the nucellus, degenerate and are absorbed by the growing embryo. The endosperm, a tissue that provides nutrients to the developing embryo, may also be present in some seeds. The seed gradually matures, and the seed coat becomes fully developed and hardened.

In conclusion, the correct answer is option 'C', the outer integument. The outer integument of the ovule differentiates and forms the seed coat, which protects the developing embryo and stored nutrients inside the seed during seed development.