If you inoculate someone, you try to make him immune to a disease by injecting a little dose of it, so his body can make antibodies to fight it off. When you were little you probably got a vaccine to inoculate you against smallpox.
When inoculate first came into English in the 15th century, it referred to inserting a bud onto another plant. Now you’re more likely to hear it used to describe the process of building up immunity to a disease by giving someone a vaccine, which also involves the insertion of foreign matter. You can also inoculate someone metaphorically, with ideas.