Recently, researchers from Carnegie Mellon University, a worldwide leader in brain science, have published one of the first evidence-based accounts of how mindfulness training actually works to reduce stress and improve physical and mental health on a biological basis. Scientists have long known that mindfulness (e.g. yoga, meditation) reduces the risk of stress-driven illnesses (e.g. heart attacks, strokes) and improves mental health. However, until very recently, it was unclear how mindfulness biologically provided all those benefits.
I won't bore you with the chemical names, but suffice it to say that mindfulness works by reversing the chemical processes induced by stress. For instance, stress causes a decrease in activity in the area of the brain called the pre-frontal cortex - the part of the brain that is responsible for conscious thinking. At the same time, stress increases activity in the amygdala, hypothalamus and anterior cingulate cortex - areas of the brain that trigger our natural stress response (e.g. increased blood pressure, suppression of the hormones that make us sleep). It is this stress response that contributes long-term to poor physical and mental health.
So by participating in mindfulness exercises, we can help reverse the biological effects of stress on our minds and bodies. Mindfulness exercises can take many forms, such as yoga or meditation, or perhaps something simpler like walking in the woods or light exercise, or even one of a small handful of mindfulness apps. (I must say that many "mindfulness apps" are junk, but I do enjoy the app Happify very much and find that it is based on sound science.)
The bottom line is that researchers from Carnegie Mellon University, a global leader in brain science, have confirmed what many have testified to for decades - mindfulness exercises really do reduce stress and anxiety, improving our mental and physical health. You can learn more about this recent research from a longer article on Science Daily.