What does the thymus do and what hormone does it produce?

Thymus helps in development and maturation of T-lymphocytes of immune system.

Thymus secretes a polypeptide thymosine hormone.

There is still considerable ignorance about exactly how the thymus does its job, but it is now known that it is essential for the proper running of the lymphatic system, and that it has really carried out its major function during the first few years of life.the thymus is believed to produce thymosin, which promotes the development of antibodies, especially T lymphocytes, or T cells. The thymus stops working after puberty
The thymus is found in the upper part of the chest, where it lies just behind the breastbone. In a young adult it is a few centimeters long and weighs about 15 gm. (one-half ounce). However, this simple statement conceals the most remarkable thing about the thymus, and that is the way that, quite unlike any other organ, it is at its largest at about the time of puberty when it may weigh up to 45 gm (one and one-half ounces). In a baby, the thymus is really very large compared to the rest of the body, and it may extend quite a long way down the chest behind the breastbone. It grows quite quickly until about the age of seven; after this the thymus continues to grow, but much more slowly until puberty. After the age of puberty the thymus starts to shrink in size--a process called involution--until in an elderly person there may be no more thymus tissue present apart from a bit of fat and connective tissueThymus hormones travel through the bloodstream and continue to exert their influence over the departed T cells. Thus, the thymus can be considered to be a true endocrine gland-- carried to another part of the body where it will have its effect. We know that the thymus continues to secrete hormones and to 'train' and export T cells until late in life. After puberty it diminishes in size because it is no longer concerned with growth.