Mindfulness is a practice integrated in various religious and secular traditions, from Buddhism and Hinduism to yoga and, more recently, non-religious meditation. The practice has been used for over thousands of years in the east, in recent years it has gained popularity in the west.
One of the biggest influence on bringing mindfulness from the East to the West, at least in the last decade, was Jon Kabat-Zinn. Jon Kabat-Zinn is a Professor of Medicine Emeritus and in 1979 he founded the Center for Mindfulness at the University of Massachusetts Medical School and the Oasis Institute for Mindfulness-Based Professional Education and Training in it. His aim was to provide an alternative method to help people that were chronically ill. Inspired by the eastern practice he created the Mindfulness-Based Stress Reduction program, with the intention of helping anyone looking to reduce their levels of stress.
Jon Kabat-Zinn learned about and studied mindfulness under several Buddhist teachers, including Thich Nhat Hanh (an influential and popular figure in Western mindfulness himself). This gave him an Eastern foundation in mindfulness that he integrated with Western science to develop MBSR.