To open to the sense, to become really conscious, you have to drop out of the future and the past and remain for a time in what T. S. Eliot called "the still point of the turning world" — the present. The only true reality is the present.
Mindfulness is an ancient form of meditation in which one pays attention to the present moment and all that's unfolding in that moment, both within and around one. It's known also as conscious living because the person practicing it is forming an aware and intimate relationship with each moment.
When practicing mindful meditation we aren't striving to do anything, we aren't grasping, struggling, thinking, expecting, or wanting but simply letting whatever is there be there and paying attention to it in a non-judgmental way. We come to terms with reality as it is, bringing all our awareness to it, breathing with it, attending it.