Wikipedia
Samādhāna or samādhānam ( Sanskrit:समाधानम्) is a Sanskrit noun derived from the word, samādhā , and variously means – putting together, uniting, fixing the mind in abstract contemplation on the true nature of the soul, profound or abstract meditation, deep contemplation, intentness, steadiness, composure, peace of mind, clearing up a doubt or replying to the pūrvapaksha, agreeing or promising, a leading incident, justification of a statement, proof, reconciliation or eagerness.
Samādhāna, which develops mental concentration, is one of the six virtues (shad sampat) that a seeker after truth is expected to develop so as to cultivate the attitude of detachment from all selfish-ends; it develops the ability to hold the mind on a single point. For achieving this qualification the mind is required to be sufficiently trained, and is achieved by the combination of the other five virtues – sama, dama, uparati, titiksha and śraddhā. Shankara defines it as a state of poise and tranquility that the mind gains when it is trained to revel continuously in the concept of a perfect ideal, at once universal and omnipotent.
Samādhāna is the single-pointedness of the mind ; it is the state of the mind which one has with a single goal in sight which is gained on the strength of the control of the mind and the senses, with-drawl from worldly pursuits, endurance of life-pangs and faith in the scriptures and teacher’s instructions. It is one of the four requisites for realization of Brahman (sadhana Chatushtaya) that directs the energy of consciousness towards moksha ('liberation') and not towards siddhi or vibhuti ('accompalishments'). In the Mahabharata(277:6), samādhāna is explained as the absorption of meditation or as that state of mind in which one has no longer any affection for the world. In his Vivekachudamani (Sloka 27), Shankara explains that:-
सम्यगास्थापनं बुद्धेः शुद्धे ब्रह्मणि सर्वदा | तत्समाधानमित्युक्तं न तु चित्तस्य लालनम् ||the perfect establishment of the buddhi always in the pure ( nirguna) Brahman (free from all limitations) is said to be samādhāna, not the indulgence of the mind (not giving free rein to the mind to stray at will).