The science of mindfulness
Our brains have an in-built capacity for sustained attention, but this is weakened by competing demands for our attention in our busy, complex lives, surrounded by distractions. Formal mindfulness practices involve training the mind to focus on a single object, such as the breath, body sensations, sounds etc. This activates and strengthens the neural networks associated with sustained attention.
New developments in neuroscience show that our brains are malleable – as we use our minds, physical changes happen in the brain. For example, one study of London taxi drivers showed the regions of their brains associated with navigation were larger than normal, and that the longer they had been taxi drivers, the larger these regions were. 
Studies have shown how meditation practice leads to changes in the brain that enhance attention and various other functions. A study of long-term meditators found that:
‘Brain regions associated with attention, interoception [awareness of body sensations] and sensory processing were thicker in meditation participants than matched controls, including the prefrontal cortex and right anterior insula. Between-group differences in prefrontal cortical thickness were most pronounced in older participants, suggesting that meditation might offset age-related cortical thinning.’ 
And another study showed that changes happened over just eight weeks of mindfulness training:
‘The results suggest that participation in Mindfulness-based Stress Reduction (MBSR) is associated with changes in gray matter concentration in brain regions involved in learning and memory processes, emotion regulation, self-referential processing, and perspective taking.’ 
 Maguire et al (2000). Navigation-related structural change in the hippocampi of taxi drivers. Proceedings of the Academy of Sciences.
 Lazar et al (2005). Meditation experience is associated with increased cortical thickness. Neuroreport.
 Holzel et al (2011). Mindfulness practice leads to increases in regional gray matter density. Psychiatry Research.