Mindfulness and meditation
When we are meditating, we are effectively reducing the noise and fluctuations of a mind otherwise caught up with life and all its distractions. When we are fully engaged in a method of practice, whether it be following the breath, contemplating a huatou or gong'an (koan), the mind has no space for thoughts of the present or the future. The method is all there is.
At such times we are entirely in the present and the mind is given a chance to experience the awareness of "now." Like the marathon runner training for the big race, when we meditate diligently for a long time, the mind becomes habituated to facing the daily clamor of life with equanimity and stamina, not being tossed and turned around by obstacles and events. The ability to stay on track, nurtured by meditation, contributes to one's ability to be immersed in the present, and to deal with it effectively.
Mindfulness and cultivating wisdom
When we cultivate wisdom, we begin to learn how to distinguish the real from the illusory, the true from the false, and the precious from the useless. Like a sword cutting through the underbrush before us, wisdom allows us to find the middle way between craving everything life has to offer and being indifferent to it all; it is being able to invest our time and effort in only those things that benefit ourselves as well as others in accordance with the Dharma.
By cultivating wisdom we also cultivate compassion, the ability to empathize with the suffering of others and to respond without self-interest. Based on a foundation of loving-kindness, compassion in daily life is best practiced as a "hidden" virtue. It is simply there as a potential to think wholesome thoughts acts, speak kind words, and perform beneficent acts. As such, compassion is also mindfulness.