It is practiced by the Kagyu, Gelug and Sakya schools of Tibetan Buddhism, and possibly also by derivative Vajrayana orders in China, Russia and Japan. (The Nyingma and Bön traditions and their derivatives practice a corollary but distinct method of direct introduction called Dzogchen or Ati Yoga.
The contemporary philosopher Oscar Ichazo has introduced a third method of direct introduction which he calls the Velocity Method.)
The term Mahamudra is often explained as referring to the uncontestable validity of the experience. For example, if a document bears the Great Seal of the Emperor, then there is no question as to the authenticity of that document. Similarly, it is said that during the genuine experience of Mahamudra, one has no question that one is directly glimpsing the nature of Mind (Buddha Nature or Tathagatagarbha) and that recalling and stabilizing this experience leads to profound certainty and eventual Enlightenment.
The meditative practice of Mahamudra is divided into 2 distinct stages: shamatha (concentration) and vipashyana (mindfulness). The first can be described as concentration whereby one learns, patienty, to "tame" or focus their mind or mental awareness; after the power of effortless concentrated consciousness had been achieved, the second stage of vipashyana can begin. During this part of the exercise, the practicioner's mind is trained to witness sensory, emotional and mental processes without attachment, ie. while observing images, sounds and sensations, a meditator's consciousness disidentifies from any particular object, having as the result bodhi or enlightenment.
Mahamudra, belonging to a class of non-energetic yogas (unlike 6 yogas of Naropa), is the most widespread meditative practice in Tibetan Buddhism. Essentially, it is equal to the Soto Zen practice of meditation, with shamatha and vipashyana named in Chinese chih and kuan.
See also: mudra