The more intimate your relationship is with your airplane, the better prepared you are to provide the airplane with a long, healthy life and, more importantly, you will be more acutely aware of when something is not quite right. You are much more likely to be able to accurately diagnose a problem quickly if you know the intimate details of the systems and, as a result, you may be able to prevent an emergency by detecting issues early.
A great time to learn more about or to get a refresher on the intricacies of your airplane’s system is during the annual inspection. Ask your mechanic if you can spend a day with him or her to help or even just observe the inspection. As a renter, it may be a little bit more difficult to get into the shop, but some mechanics really enjoy educating pilots and if you offer to help out in the shop in return for some education you may get the green light.