The following definition of mindfulness is taken from Wikipedia:

Mindfulness is a technique in which a person becomes intentionally aware of his or her thoughts and actions in the present moment, non-judgmentally. It plays a central role in Buddhism, with Right Mindfulness being the seventh element of Noble Eightfold Path, the practice of which is considered a prerequisite for developing insight and wisdom. In a secular context, mindfulness is attracting increasing interest among western psychiatrists as a non-pharmacological means of dealing with anxiety and depressive mood states.

Right mindfulness (often also termed Right Meditation) comes in a variety of forms. One example of mindfulness is to mentally give a verbal label to each inbreath and outbreath during sitting meditation. So, each time one breathes in, one thinks “rising”, and each time one breathes out, one thinks “falling”. In this type of meditation, the breath serves as a tether that the practitioner uses to bring his or her awareness back to the present moment.

By residing more frequently in the present moment, practitioners begin to see both the inner and outer aspects of reality. Inner reality may unfold as one sees that the mind is continually chattering with commentary or judgment. By noticing that the mind is continually making commentary, one has the ability to carefully notice those thoughts – and decide if those thoughts have value.

Most often, mindful people realize that “thoughts are just thoughts” – the thoughts themselves have no weight. People are free to release a thought (“let it go”) when they realize that the thought is not concrete reality. They are free to observe life without getting caught in the commentary.

As one more closely observes inner reality, one finds that happiness is not a quality brought about by a change in outer circumstances, but rather by realizing happiness starts with releasing attachment to thoughts; thereby releasing “automatic” reactions toward pleasant and unpleasant situations or feelings.