Mindfulness is the intentional, accepting and non-judgmental focus of one's attention on the emotions, thoughts and sensations occurring in the present moment, which can be trained by meditational practices derived from Buddhist anapanasati. It has been popularized in the west by Jon Kabat-Zinn with his Mindfulness-Based Stress Reduction (MBSR) program at the University of Massachusetts Medical School in Worcester, Massachusetts.
Organizations:
Center for Mindfullness in Medicine, Health Care, and Society, University of Massachusetts Medical School: http://www.umassmed.edu/cfm/
Wikipedia articles on mindfullness:
Mindfullnes: http://en.wikipedia.org/wiki/Mindfulness
Mindfullness (psychology): http://en.wikipedia.org/wiki/Mindfulness_(psychology)
Mindfullness meditation: http://en.wikipedia.org/wiki/Mindfulness_meditation
Mindfullness-based Stress Reduction: http://en.wikipedia.org/wiki/Mindfulness-based_stress_reduction