Meditation techniques of one form or another have been used for thousands of years. Practitioners claim a wide range of physical and psychological benefits - many of which have now been verified by controlled scientific studies. Modern scientific techniques, such as fMRI and EEG have been used to observe neurological responses during meditation.
A 2014 review study, looking back at 47 trials with 3,320 participants, found that there are benefits - but usually moderate - (though comparable with other treatments.)
See : Meditation Programs for Psychological Stress and Well-being: A Systematic Review and Meta-analysis JAMA Intern Med. 174(3): 357–368.)
Other research groups are more sceptical :
“Many uncertainties surround the practice of meditation. Scientific research on meditation practices does not appear to have a common theoretical perspective and is characterized by poor methodological quality. Firm conclusions on the effects of meditation practices in healthcare cannot be drawn based on the available evidence. Future research on meditation practices must be more rigorous in the design and execution of studies and in the analysis and reporting of results.”
Source :US agency for Healthcare Research and Quality Evidence Report, Technology Assessment , Number 155.
Either way, the neurological mechanisms by which meditation might actively achieve psychological and physical benefits are completely unknown.