The “Introduction to Mindfulness Meditation” from Gil Fronsdal and the Insight Meditation Center provides a great introduction to mindfulness and the various ways we can apply mindfulness in meditation. Mindfulness is not just watching the breath, but a clear awareness of whatever arises, including bodily sensations, thoughts, and emotions. You can find the introduction here: Introduction to Mindfulness Meditation
Joseph Goldstein was one of the pioneers in bringing the practice of mindfulness to the West. His book Mindfulness: A Practical Guide to Awakening is an excellent source for people interested in learning more about mindfulness meditation. This article provides a chapter from that book that lays out several important qualities of mindfulness. You can find the article here: The Four Foundations of Mindfulness
The description of mindfulness in Sarah Doering’s article on the five faculties is very helpful, especially her description of the importance of interest in what we observe in fostering mindful awareness. You can find her article here: The Five Spiritual Powers