A slow, deep breath is the simplest, most concrete thing you can do for your health and performance. It immediately signals to the amygdala (the emotion center in the brain) that 'everything is OK', thereby calming the tense grip anxiousness has on the body and mind.
When you slow down your breath, you are increasing the amount of oxygen available to your body and brain, which affects how hard your heart has to work to pump blood throughout your body.
Slowing your breathing is the best way to increase HRV (heart rate variability), a measure of autonomic tone. HRV is a proxy and one that is in debate amongst researchers – however, there is no question that control of breathing is an effective means of lowering anxiety, calming the body, and improving health.