I'm occasionally asked to define mindfulness, and after stumbling on it one time too many, decided that I needed to come up with an elevator pitch-level description.
I've settled on "detached, deliberate attention" as the briefest description I can come up with (and remember). Detached is an important element of mindfulness because you want neither to be surprised by what you see, nor have your preconceptions lead you to see only what you expect or want to see. The term deliberate is important because mindfulness require intentionality: you mean to focus on something in a particular way, rather than just causally (or rather than ignoring it altogether).
Of course, there are many definitions of it: Jon Zabat-Zinn, the founder of mindfulness-based stress reduction therapy (MBSR), writes that
mindfulness has to do with particular qualities of attention and awareness that can be cultivated and developed through meditation. An operational working definition of mindfulness is: the awareness that emerges through paying attention of purpose, in the present moment, and nonjudgmentally to the unfolding of experience moment by moment.
Bishop et al (2004) propose an "operational definition" of mindfulness that has two components:
The first component involves the self-regulation of attention so that it is maintained on immediate experience, thereby allowing for increased recognition of mental events in the present moment. The second component involves adopting a particular orientation toward one’s experiences in the present moment, an orientation that is characterized by curiosity, openness and acceptance.
Actually, I'd completely forgotten about this, but in my article on futures thinking and weight loss I described mindfulness as "the ability—or more accurately, cultivation of the ability—to closely observe the present, without preconceptions and filters, with an attitude of calm." That's actually pretty good, too.