What is mindful focused self-awareness from a cognitive science perspective? Focused mindful self-awareness (Google talk Jon Kabat-Zinn) are common activities, used to help patients of a variety of mental illness of different degrees - with some evidence of healing (Dr. Jeffery Schwartz).

From a cognitive science perspective, what is this focused mindful self-awareness?
I think your asking a psychologically healthy spiritual question. Psychologist are told to promote spirituality and many concepts from religion have affected current day therapies.

Bishop, Lau, and colleagues (2004) offered a two-component model of mindfulness:
The first component of mindfulness 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.
In this two-component model, self-regulated attention (the first component) involves conscious awareness of one's current thoughts, feelings, and surroundings, which can result in metacognitive skills for controlling concentration. Orientation to experience (the second component) involves accepting one's mindstream, maintaining open and curious attitudes, and thinking in alternative categories (developing upon Ellen Langer's research on decision-making).

-wikipedia mindfulness
As a student of psychology, psychiatry and neuroscience I will give you my perspective of the cognitive science understanding of mindfulness. Then I'll give a less biased published view of a professor of psychology.
When I was 14 the church I belong to at the time was helped to be run by my Father. He built a pool for the church and right before the beginning of the High School semester we laid down concrete. For some reason the baseball coach decided to help us in exchange for some extra concrete for his field. I did not like laying concrete. The raking, bull float and constant worry that it would harden in an untenable way. To make matters worse the coach talked my dad into removing his partitions which would have made many small slabs around the pool into one giant slab. Anyone who knows about concrete in the south would immediately know that this means its going to crack and have to be sealed eventually. At the end of the day my muscles were give out and i lost my balance and my hand went into the crete a couple of times. In addition even though I count that day one of the times I worked extremely hard for no pay the coach had decided to call me various names and stuff. On the way home my father lost his temper with me. My grandparents put things into perspective.
Thier common way of doing it is consistent with Acceptance and commitment therapy (ACT) which uses mindfulness:


Cognitive defusion: Learning methods to reduce the tendency to reify (inforce negative and self defeating schema see this example from The Help) thoughts, images, emotions, and memories.

Acceptance: Allowing thoughts to come and go without struggling with them.

Contact with the present moment: Awareness of the here and now, experienced with openness, interest, and receptiveness.

Observing the self: Accessing a transcendent sense of self, a continuity of consciousness which is unchanging.

Values: Discovering what is most important to one's true self.

Committed action: Setting goals according to values and carrying them out responsibly.



-wikipedia ACT
They said, God loves you we love you don't worry (Observing the self,Contact with the present moment,Values), don't be upset at him (Committed action) he's tired and isn't thinking clearly (Acceptance), of course you worked extremely hard today but your father wasn't watching you I was (Cognitive defusion), everyone loses their balance at some point especially during the last few hours it was easily correctable (Cognitive defusion). This common sense, non-judgemental, encouraged me to consider the situation rationally, accept the fact that I was limited and my father was limited and not hold ill feelings toward him.
Evangelical Christianity is all about &quot;Contact with the present moment&quot;, &quot;Observing the self&quot;, and &quot;Values&quot;. Services are chocked full of religious based phrases which lead people to experience a contact with the present moment through experiencing forgiveness, justification and cleansing of the past. God loves you it doesn't matter what you've done in the past your forgiven now, forget the past, your a new person in Christ now, there is hope for you, &quot;Everything is working out for my good and for God's Glory&quot;. While we don't have all of ACT down if you go to such a church you will certainly learn to live in the present by allowing God to deal with you past. Such may be the case in other religions but I do not know.
The following is an exerpt from Dr. McFadden's Mindfulness, vulnerability, and love: Spiritual lessons from frail elders, earnest young pilgrims, and middle aged rockers:

Raised a nominal Roman Catholic, with no concrete plans for entering the ministry, John McFadden went on to serve as senior pastor of two large United Church of Christ (Congregational) faith communities for a total of 32 years. As a result, I became a “minister's wife” and received the blessings of friendship with many older men and women who were my first teachers about aging with grace. These lessons accrued through the years and inspired my academic exploration of the psychology of religion and aging. From the beginning, when we were 23 years old with no clue how to be a minister or a minister's wife, to the time my husband retired from ministry to a beloved congregation in 2006, it was the old people who reached out to us with a multitude of kind and generous acts. In our age-segregated society, if I had married an accountant, a dentist, or a professor, I probably never would have developed such treasured friendships with older adults.
My sense of time stops, and my identity as “Susan McFadden, Ph.D., Psychology Professor, wife, mother, blah blah blah” disappears as I crouch to grasp a hand, gaze at a face, and say “peace be with you.” Regardless of whether the person whose hands I hold can reply with a verbal blessing, the moment feels powerfully imbued with holiness. I face my own vulnerability, for one day I may be demented or immobilized by stroke. In that large, crowded room at the nursing home, I am uplifted by love given and love received.
Although we cherish our worship experiences at the nursing home, most of the time we worship in a bar with pierced and tattooed young adults. The service starts at “10:30-ish,” the pastor sits on a barstool like everyone else, and music consists of everything from alt-rock to bluegrass. This bar is a long way from the staid Presbyterian church of my youth and the Congregational churches John served in his ministry. We decided that his leaving the ministry afforded us the possibility of doing something completely different and exploring a new way of being in Christian community. Called the “emergent church” by some scholars, these groups attract people who have been described as “avant-garde youth and aging hippies” (Byassee, 2006: 20). Many have fled “big box” Evangelical churches with their “Jesus goes to Vegas” style of worship and their political allegiance to conservative causes. They are seeking an authentic way of holding one another accountable to love God and one another.
Like worship at the county nursing home, worship at the bar evokes feelings of mindfulness, vulnerability, and love. The mindfulness derives from the desire to be fully present to the mostly young adults worshipping in that odd place, with its pool tables and dart machines. John and I do not want to play the role of know-it-all baby boomers, but rather to join these persons as fellow pilgrims. On the other hand, he is often asked to schedule a time for coffee and theological conversation, while I am frequently asked for advice about academic matters. Thus, mindfulness involves intentional awareness of how best to be respectfully present to others and to humbly offer whatever we have gained from our experiences that might be helpful. Vulnerability is located in the conviction that we have much to learn from these young adults, and that our own faith can grow as a result of knowing them and hearing their tales of spiritual journeys that sometimes have moved through treacherous territories of drug abuse and lost-ness. This little community often speaks about love, and the challenge of following Jesus' commandment to “love one another” in a world full of enticements to love self first and foremost, as well as repeated messages that the self is not good enough, attractive enough, rich enough, or sane enough to be loved by another person.
All of these people—old and young—have taught me about relational mindfulness, vulnerability, and love. Their intensity, whether born of their conscious decisions to live by different values than those of the prevailing culture, or their un-chosen suffering, invites mindful engagement. All remind me about my various vulnerabilities, ranging from the existential reality of my finitude to my everyday struggles to live faithfully. Most importantly, they teach me new ways of giving and receiving love.

McFadden, S. H. (2008). Mindfulness, vulnerability, and love: Spiritual lessons from frail elders, earnest young pilgrims, and middle aged rockers. Journal of aging studies, 22(2), 132-139.