The Pali/Sanskrit word samādhi, usually translated as “concentration,” is made up of three parts, a verbal root and two prefixes (sam+ā+dhi). The last part, dhi, is a noun form derived from the verbal root dhā, meaning “to put or place.” The prefix ā gives direction and suggests “placing upon,” and the prefix sam means “gathering or bringing together.” When combined and used in a Buddhist context, these elements add up to the sense of “unifying the mind and placing its awareness upon a particular object.”
Traditional sources also emphasize that the mind focuses on a single (eka) point (agga), and “one-pointedness” (Pali, ekaggatā; Skt. ekāgratā) is another common way of defining samādhi. The mind is actually always focused on a single object in any given moment, but it habitually moves rapidly—and sometimes restlessly and apparently randomly—from one object to another. You may have noticed this!
The practice of developing concentration as a meditative skill begins with intentionally directing the mind to a chosen object, such as the breath, and holding it there steadily over multiple successive mind moments. This is not easy to do at first, as reflex draws our attention to novel and distracting sights, sounds, sensations, or thoughts. Keeping the mind grounded on one thing can seem boring, futile, or frustrating.
With practice, however, the mind wanders off its object of meditation less often, staying away for less time before its meandering is noticed and attention is called back to the breath. The body becomes progressively more relaxed, breathing naturally slows down and gets more subtle, and the mind begins to feel increasingly peaceful, stable, lucid, and capable. With such enhanced focus one can now look more closely at the flowing stream of consciousness, or one can proceed to deeper levels of samādhi.
A tipping point can be reached when the experience of the concentrated mind itself becomes more compelling than the allure of external objects, and a state of absorption known as jhāna gradually develops. The mind becomes tranquil but alert, with neither too much nor too little energy, and finds an equanimous stance that neither favors nor opposes anything but rather rests with quiet confidence on its object. A growing sense of well-being ensues and slowly matures into a state of profound equanimity. The mind in this state is said to be luminous, malleable, cleansed of its impurities, and thus able to see things clearly. Now the process of developing wisdom can begin.