Mindfulness is a way of living that emphasizes thinking over action. In emphasizing thought, mindfulness instructs one how to take hold of the mental experience so that one can have a better life and more happiness.
All humans think and act of course. Most people however judge circumstances, themselves, and others based on the concrete, physical results of actions. If those actions bring about results that are pleasing then those actions are judged as good; if the physical results are painful or the opposite of one's wishes then they are judged as bad.
Mindfulness however says that pleasure and pain, success and failure, and all of the dialectics* of life have much more to do with how we think than the tangible circumstances that we encounter throughout the 168 hours of every week of our lives. Instead of living our lives based on the physical world that we live in, mindfulness directs us to look beyond the packaging of the pains and distractions of the physical world to discover the opportunities for joy, mastery, connection, and healing that lay there ready for the taking. Mindfulness teaches us how to avoid the traps that the superficial, physical world lays for us. At the same time, mindfulness allows us to love life and all of the pleasures that it contains.
Looking beyond the physical and focusing on the mental experience is reflected in many places in Jewish thought and literature. It was Rabbi Yehuda HaNasi who taught us that instead of looking at the bottle one should instead look at what lies inside (Avot 4:20). This was his poetic way of telling us to avoid being seduced by superficial trappings that may be pleasing to the eye or soothing to the body. Lest one assume that pleasure and comfort is taboo, we are taught over and over again that God made the universe for us to deeply enjoy.
*Dialectics is a Greek word that means 'the study of opposites'. Life is made up of many, many sets of opposites such as cold and hot, cook and bad, life and death, and freedom and slavery. Finding the best balance between the two opposites is a key to a happy life.