I'm confused about the difference between active and passive immunity

Active immunity occurs when an individual develops immunity against a specific antigen when they are exposed to it - your body reacts by producing memory cells that provide long lasting immunity against that specific antigen. This happens when you get a vaccination for instance - your body is exposed to a specific antigen (e.g. MMR) - then your body forms memory cells to protect you from that disease. 

Passive immunity is slightly different, because the individual becomes immune to a specific antigen thanks to antibodies that are already ready-made. A good example are antibodies that can pass from mother to foetus via the placenta, or via a mothers milk during suckling - the baby isn't actively producing these antibodies - they are simply being passed on and stored for later use if the need to fight a specifc antigen arises. Passive immunity is generally more short-term vs active.