“Most of us are rarely in the present moment.
We focus on past experiences and emotions.
We are constantly thinking about what might happen next.
Humans are ‘bundles of habits’.
We are often ‘on auto pilot’.
We are often unaware of what we are doing”.*
Mindfulness meditation involves attention to breathing and focusing on the present moment, with non-judgmental awareness of thoughts and feelings that arise.
An objective of this practice is to train ourselves to recognize and get beyond random thoughts and distractions, and also biases and preconceptions, and come to see ourselves and things around us more clearly, with active attention to and appreciation of the present.
Prominent teachers include the Vietnamese Zen master Thich Nhat Hanh and the American Jon Kabat-Zinn.
In Buddhist tradition, mindfulness may be a path toward enlightenment.
For religious naturalists, mindfulness can be recognized as a general attitude that can contribute to the type of awareness and appreciation of the natural world that can prompt a sense of reverence. 
It involves the difference between knowing about things and being mindful of them.
As is discussed in an essay by Michael Barrett, developing a long-term attitude of mindfulness can be part of what some religious naturalists do as part of their personal spiritual development.
Links
Oxford Mindfulness Centre, Oxford University
Plum Village Mindfulness Practice Center (Thich Nhat Hanh)
Jon Kabat-Zinn
…..Home site
…..Bill Moyers video
Mindfulness (the basics, at the Psychology Today website)
How to do Mindfulness Meditation, Shambala Sun
Mindfulness: A Short Course
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* Quote: from a short video at Mindfulness.net