The essential identity of the Atman and brahman is the most important tenet of advaita. brahman is the substratum on which all phenomena are experienced, and also the antaryAmin, the One Lord who dwells in all beings. The innermost Atman, the real Self, is the same as this antaryAmin, and identical to brahman. Liberation (moksha) consists in realizing this identity, not just as a matter of literal or intellectual understanding, but as something that is to be grasped by the individual in his/her own personal experience. Yogic practices help in the road towards such realization, because they help the seeker in practising control of the senses, and in directing the antahkaraNa (the 'internal organ' - consisting of the mind, intellect, awareness and I-ness) inwards. The practice of ashTAnga-yoga is recommended to seekers by teachers of advaita. The seeker has to be equipped with requisite qualifications - qualities such as patience, forbearance, ability to focus one's concentration in an intense manner, an ability to discriminate between the Real and the non-Real, dispassion, and a desire for liberation. However, it is important to remember that moksha is not a result of mere ritualistic practice. Being identical to brahman, moksha always exists. Ritualistic practices help only to the extent of achieving citta-Suddhi, and in developing the above-mentioned qualities.
advaita is a non-dual teaching. When asked why duality is perceived in this world, advaita has a multi-pronged answer to the question. The world of multiplicity can be explained as due to mAyA, the power of creation wielded by the Creator, who is therefore also called the mAyin. From the point of view of the individual, the perception of duality/multiplicity is attributed to avidyA (ignorance) due to which the unity of brahman is not known, and multiplicity is seen instead. This is akin to the false perception of a snake in a rope. When the rope is known, the snake vanishes. Similarly, on brahman-realization, the world of multiplicity vanishes. This does not mean that the individual's ignorance creates the external world. However, the perception of multiplicity in the world, instead of the One brahman, is due to avidyA, i.e. ignorance. When avidyA is removed, the individual knows his own Self (Atman) to be brahman, so that there is no more world and paradoxically, no more individual. Here, the Self alone IS. Removal of avidyA is synonymous with brahman-realization, i.e. moksha. http://www.advaita-vedanta.org/avhp/ad_faq.html
What then of the human self, the jIva? It is here that advaita comes up with the most radical answer, one that is unacceptable to all other schools of vedAnta. According to advaita, what is called the universe is in reality not other than brahman. Similarly, what is called the jIva is in reality, the Atman, which is also nothing other than brahman Itself. The real jIva is the Atman, which is unchanging, ever free, and identical with brahman. This is said on the basis of upanishadic passages where the Atman is explicitly equated with brahman. This equation of Atman with brahman is also explained by means of adhyAropa-apavAda. By sublating the superimposition of human shortcomings and attributes on the Atman, the pure Atman, the substratum, shines forth as brahman Itself. The mani-fold universe and the individual self, which considers itself bound, are both superimposed upon that Transcendental Reality which is brahman. Once the superimposition is understood for what it is, the individual is no more an individual, the universe is no more the universe - all is brahman.
This doctrine of advaita should not be misinterpreted to mean that the human self is in and of itself God, without any qualification whatsoever. SankarAcArya most emphatically asserts that such is not his intention. On the other hand, he is at great pains to point out that one who is desirous of moksha needs to overcome his human shortcomings in order to achieve full liberation. Sankara prescribes rigorous prerequisite qualities for the person who is to study vedAnta. These form the practical aspect of the effort to rise above and sublate the characteristics of the human jIva, in order to understand the Atman/brahman. The non-dual reality of the Atman is revealed to the intense seeker, as an experience that defies words. One might call it a mystic experience of brahman, in which to know brahman is to be brahman. Thus, rather than being atheistic or non- theistic, advaita vedAnta is meta-theistic: it points to the basic underlying Reality of all, including what humans call God, what humans call the universe, and what humans call human. This Reality is the unchangeable brahman. http://www.advaita-vedanta.org/avhp/ad-phil.html