You will often hear the term insightful comment or insightful observation. What English teachers want from students writing papers is insightful analysis––one that sees beyond the obvious to express an original thought.
With this word, remember in- and -sight-. When you have the ability to look (sight) inside (in) something––a painting, a discussion, a situation––and find what others aren't seeing, you are being insightful. An insightful person is someone capable of deep, insightful thinking.