Does vaccination make the immune system "lazy"?
Contrary to many beliefs our immune system needs no "training". It is permanently active and confronted with dozens to hundreds of antigens in our food, from dust we inhale and so on. This all happens to protect our body from the environment and the immune system is pretty efficient with that and certainly it is not getting lazy.

By vaccinating against a certain disease, you generate immunogenic memory against this disease. When you then get exposed to the disease, this memory helps to speed up the immunogenic reaction against the disease - ideally you are not getting sick, in some cases the progression of the disease is much milder.

Further reading:


Wikipedia on adaptive immunity
The front line of host defense from Janeway at the NCBI Bookshelf