Active immunity is the result of being exposed to an antigen (a virus or part of a virus). For example, after you recover from a case of the flu, you can no longer be infected with that particular strain because the memory cells in your immune system will be able to recognize it and produce antibodies if it enters your body again. Passive immunity doesn’t last as long because with this kind of immunity, you are receiving antibodies from an outside source rather than producing them yourself (your body hasn't learned to create them, so it can't sustain the response). A common example of this is when antibodies are passed from a mother to a child through milk. This case study is an example of passive immunity: the calves that don’t get their mother’s milk also don’t get antibodies from the mother to protect them against viruses that cause diarrhea.
Natural (or innate) immunity is a nonspecific response that occurs regardless of what the invading substance is—it occurs immediately, before the body has identified the virus. In contrast, acquired immunity (or adaptive immunity) is the result of being exposed to antigens that the body has identified. The example is actually talking about artificial immunity because antibodies are being delivered through the milk. However, the response is specific to the virus, so this can be considered acquired immunity as well.