The word student is often associated with school because it is a place of learning, and people there are studying about various fields but being a student is not that simple. You can have many places to learn from, things to experience and see, and have mistakes that you can reflect on.
Student of life means that you are learning from various experiences and things that are happening around you. You are not restricted to learning new things only in school because life as a whole is your learning field. They have life as the source of their learnings and knowledge, and life is profound, anything can happen, and that means you can learn anything you want to learn if you are a student of life.
Experience goes hand in hand with life. Experience can include love, mistakes, and many things, and people who tend to reflect on their existing experiences are students of life. They are people who have their eyes wide open and have already thought twice about whether to repeat the same thing that happened or not.