The word “samatha” means stopping. It is akin to the sanskrit term “Samadhi”. It is the practice of concentrating the mind on one object exclusively until the mind and its object are unified.
The breath is the most common object of samatha because it is easily accessible to all personality types. Other objects include colored disks, mantras, and sensations.
In Buddhist meditation practice, samatha is what leads to the unified mental states known as jhana (skt:dhyana). It is in these states that the Buddha remembered his previous lives and discovered the ancient path to Nirvana. However, jhana by itself is not the whole of the practice. Once the mind is sufficiently concentrated, the meditation practice changes to what is known as vipassana, or insight meditation.
Vipassana is the practice where you look at the phenomena of your experience in light of their impermanence, dukkha, and insubstantiality. This arouses insight into the nature of experience and uncovers the road to awakening.