I live a traditionally Jewish life. Twenty years ago, I was encouraged to go to a Buddhist mindfulness retreat. I was very much inspired and changed from having heard what the Buddha taught. The practice of mindfulness is the practice of paying attention in every moment of one's day. It's the balanced recognition of the truth of the moment.
Mindfulness is also a capacity of mind that everybody has.
It isn't a mantra or a visualization, it isn't about having a mind empty of thoughts. It's one of those things that we need to remember rather than learn how to do, which for me is really an important differentiation. In the mindfulness classes I teach, we sit quietly for 40 minutes, then we talk for another hour. What people are doing when they are sitting quietly is trying to pay attention moment to moment to their experience. The practice is to try to stay awake and aware of the breath coming in and out of the body and the sensations of the body.