Your thymus is the source of T-cells, the varied workers of the immune system. As you age, the thymus involutes - degenerates - and production of new T-cells fades away. Calorie restriction (CR) slows this process, which is no doubt one of the ways in which it improves immune response: "Aging of thymus is characterized by reduction in naive T cell output together with progressive replacement of lymphostromal thymic zones with adipocytes. Determining how calorie restriction (CR), a prolongevity metabolic intervention, regulates thymic aging may allow identification of relevant mechanisms to prevent immunosenescence. Using a mouse model of chronic CR, we found that a reduction in age-related thymic adipogenic mechanism is coupled with maintenance of thymic function. The CR increased cellular density in the thymic cortex and medulla and preserved the epithelial signatures." The paper then goes into some detail as to the controlling biochemical mechanisms and gene expression that accompanies these changes.

Link: http://www.ncbi.nlm.nih.gov/pubmed/19648267