Samatha meditation is the most common form of meditation practice throughout history. It existed and was taught prior to the Buddha. During the Buddha's time there were several ascetics who were quite proficient in samatha and two of the Buddha's teachers had attained to high levels of the jhanas, but still not the ultimate insight of enlightenment.
Samatha: 'tranquillity', serenity, is a synonym of samadhi, concentration.
There are actually two types of meditation as taught by the Buddha. They are samatha, which is the calm, tranquil technique and then there is vipassana, which is the type leading to Insight. Most meditation techniques in the Buddha’s time and before and even still today are primarily the samatha type. That is, they lead to a relaxed peaceful state and sometimes to great experiences of joy, bliss, even trance, but no ultimate Insight of enlightenment. Right Concentration primarily deals with the samatha type of meditation which is aimed at these highly concentrative states. But vipassana meditation, when done correctly, can provide the inner calm of samatha and also can lead to the Insight wisdom of vipassana. Concentration meditation techniques include many different meditation subjects. There are 40 different meditation subjects of samatha and four major techniques or foundations for vipassana. It can be direct one-pointedness concentration on a devotional figure. The common subject for beginners is awareness of breath. The meditator remains in the present moment focusing on the in and out breath of the body. The mind and body become calm and free of negative thoughts.