Jon Kabat-Zinn, who is one of the foremost thinkers in the field, describes mindfulness as "paying attention in a particular way; on purpose, in the present moment, and non judgementally". Those three elements form the core of mindfulness practice; focused intention, being in the moment and accepting whatever is in your awareness without judgment.
But what's the point?
Mindfulness developed as a way to understand what it is to be alive and to reduce unnecessary suffering. Although it's been practiced for thousand of years, Western science has only recently started to appreciate how powerful mindfulness is. Research has shown that mindfulness helps promote well-being and is useful in managing stress, depression, addiction and many other aspects of mental distress.