Why is it important to understand everything that is taught?
To understand everything that is taught is important for a few reasons. First, it is important, because often times knowledge is cumulative. This is to say that later information and material is built on top of previous material. This is especially so with the sciences, math and languages. In these subjects, to fail to learn certain things will handicap you for the rest of your study. Hence, it is imperative to learn the basics well.
Second, learning difficult things is an exercise in mental exertion. These are the times when you are stretched academically. Through these experiences you will get smarter and learn to think critically.
Finally, learning for the sake of knowledge itself is a noble endeavor. If you an develop this, you will be a great academic.