Mindfulness originally comes from Buddhist teachings, it's basically learning to keep the mind fully in the present, not looking back at the past or anticipating the future. Being mindful of the "now" is said to reduce stress etc.
Nowadays, mindfulness training involves learning to become aware of mind, body and emotions and there are lots of different versions of it. It's taught within Yoga, meditation, tai chi, a few new agey type of places, life coaching, hypnotherapy, there is also mindfulness based cognitive behaviour therapies, mindfulness based teacher training, the list goes on. I'm surprised that you hadn't come across it sooner.
The Power of Now by Eckhart Tolle is a good book that is very similar to the mindfulness way of thinking.