Mindfulness meditation and related techniques are intended to train attention for the sake of provoking insight. Think of it as the opposite of attention deficit disorder. A wider, more flexible attention span makes it easier to be aware of a situation, easier to be objective in emotionally or morally difficult situations, and easier to achieve a state of responsive, creative awareness or "flow".
One theory, presented by Daniel Goleman & Tara Bennett-Goleman (2001), suggests that meditation works because of the relationship between the amygdala and the prefrontal cortex. In very simple terms, the amygdala is the part of the brain that decides if we should get angry or anxious (among other things), and the pre-frontal cortex is the part that makes us stop and think about things (it is also known as the inhibitory centre).
So, the prefrontal cortex is very good at analyzing and planning, but it takes a long time to make decisions. The amygdala, on the other hand, is simpler (and older in evolutionary terms). It makes rapid judgments about a situation and has a powerful effect on our emotions and behaviour, linked to survival needs. For example, if a human sees a lion leaping out at them, the amygdala will trigger a fight or flight response long before the prefrontal cortex responds.
But in making snap judgments, our amygdalas are prone to error, such as seeing danger where there is none. This is particularly true in contemporary society where social conflicts are far more common than encounters with predators, and a basically harmless but emotionally charged situation can trigger uncontrollable fear or anger — leading to conflict, anxiety, and stress.
Because there is roughly a quarter of a second gap between the time an event occurs and the time it takes the amygdala to react, a skilled meditator may be able to intervene before a fight or flight response takes over, and perhaps even redirect it into more constructive or positive feelings.
The different roles of the amygdala and prefrontal cortex can be easily observed under the influence of various drugs. Alcohol depresses the brain generally, but the sophisticated prefrontal cortex is more affected than less complex areas, resulting in lowered inhibitions, decreased attention span, and increased influence of emotions over behaviour. Likewise, the controversial drug Ritalin has the opposite effect, because it stimulates activity in the prefrontal cortex.
Some studies of meditation have linked the practice to increased activity in the left prefrontal cortex, which is associated with concentration, planning, meta-cognition (thinking about thinking), and positive affect (good feelings). There are similar studies linking depression and anxiety with decreased activity in the same region, and/or with dominant activity in the right prefrontal cortex. Meditation increases activity in the left prefrontal cortex, and the changes are stable over time — even if you stop meditating for a while, the effect lingers.