Three of my favorite definitions (and a video):
“Mindfulness means paying attention… on purpose, in the present moment, and non-judgementally to the unfolding of experience
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“Mindful awareness is paying attention to present moment experiences with openness, curiosity, and a willingness to be with what is”
“Mindfulness means maintaining a moment-by-moment awareness of our thoughts, feelings, bodily sensations, and surrounding environment.
Mindfulness also involves acceptance, meaning that we pay attention to our thoughts and feelings without judging them—without believing, for instance, that there’s a “right” or “wrong” way to think or feel in a given moment”
According to DAN HARRIS, national news correspondent and author of 10% happier, mindfulness is actually a superpower...
The definitions above describe what I think of as informal mindfulness.
Here's a description of the distinction between formal and informal mindfulness
