Reflective writing is a type of personal response to life experiences where you think about yourself in relation to the subject material and questions being asked. Note that with reflective writing there is no right or wrong answer. The goal is to help you explore how you think, feel and behave and communicate that in writing. It allows you to be yourself and show your own personal and professional development as it relates to your area of study.
When you write reflectively, you need to go beyond just describing your experience and actually make connections between your experience, yourself, and any theories in what you are studying. Think about the 'why' and 'how' rather than just the 'what'. You may give a description (what happened), then move on to interpretation ('how' and 'why') and the result of how it has affected you. This shows you are critically reflecting, not just explaining.
Check out UNSW's examples of reflective writing with breakdowns of the different parts.