"[Mindfulness] is simply the practice of bringing ourselves fully into the present moment and continuing to bring ourselves back to it whenever we notice we've drifted away.

All of our training relies on these two practices: mindfulness and awareness. Awareness is our consciousness of being in the present. Mindfulness means "to remember" or "not to forget" to watch the mind and see when it drifts away from the present.

Of the two, mindfulness is usually emphasized more because it's responsible for maintaining the continuity of our awareness. Mindfulness means to remember again and again." 

Rebel Buddha - p. 69