Is it true that breastfeeding my child will improve his immune system?

Yes. Research has proven that breast fed babies have fewer infections than those fed formula. But be aware it they are not immune to everything. So good handwashing and avoidance are still very important.
ABSOLUTELY!!! Breastfeeding improves immunity in many ways. The mother's antibodies reduce risk of many infections, such as ear infections, gastroenteritis & coughs. It also helps to mature the baby's own immune system, increases the size of the thymus gland, reduces risk of allergies & autoimmune disease, improves response to vaccinations and decreases risk of childhood cancer. More info at http://www.Jaoa.Org/cgi/content/full/106/4/203#sec2.
Not really. But it helps your baby fight infections by giving him your antibodies, which he will get in breast milk. His own immune system will work and develop the same regardless of how you feed him. Your breast milk protects him passively, through your immune system. So while breast is best, it does not improve his immune system.