Final answer:
The thymus is the large lymphatic organ in children that is responsible for the maturation of T cells, an essential component of the immune system.
Step-by-step explanation:
The large lymphatic organ responsible for the maturation of the immune system in children is the thymus. This organ is integral in the development of T-lymphocytes, or T cells, which are essential in the adaptive immune response. During childhood, the thymus is highly active, ensuring that T cells effectively learn to discriminate between the body's own tissues and foreign pathogens. After maturation, T cells enter the lymphatic system to help protect the body against infections. Along with bone marrow, the thymus is regarded as a primary lymphoid organ due to its pivotal role in lymphocyte maturation.