A mudra is formed by holding the hands in a particular formation or posture. Buddha statues traditionally depict the Buddha holding one of these gestures. For common examples, see this article.
Some mudras, like the dhyani mudra, are used during meditation practice (especially by those who practice zazen). Others may be held during chanting or other rituals. According to the Shambhala Dictionary of Buddhism and Zen, mudras "help to actualize certain inner states. This particular mudra featured in Sabrina Mesko's book Healing Mudras: Yoga for Your Hands is called the Mudra for Tranquilizing the Mind. According to the text, it was given by Buddha to his disciples to please and tranquilize their minds. It short-circuits owrried, obsessive energy and replaces it with a calming, helpful vibration.
Working with mudras in addition to your regular sitting practice can help to focus and calm the mind and emotions. This YouTube resource provides many examples of mudra yoga: