Discrimination (Viveka) and Dispassion (Vairagya)
As a bird cannot fly if doesn't have two wings, similarly for a man who lacks of discrimination and dispassion self-realization is impossible.
Discrimination in its highest development culminates to an unwavering conviction that only Brahman (God, Spirit, Consciousness, etc.) exists as the only eternal Truth and the whole universe is an illusion.
Dispassion in top form results in complete indifference for sensory experiences, pleasures and achievements.
EXTRACTS FROM VIVEKACHUDAMANI ~ Adisankaracharya
20. A firm conviction of the mind to the effect that Brahman is real and the universe unreal, is designated as discrimination (Viveka) between the Real and the unreal.
21. Vairagya or renunciation is the desire to give up all transitory enjoyments (ranging) from those of an (animate) body to those of Brahmahood (having already known their defects) from observation, instruction and so forth.
374. Know, O wise man, dispassion and discrimination to be like the two wings of a bird in the case of an aspirant. Unless both are there, none can, with the help of either one, reach the creeper of Liberation that grows, as it were, on the top of an edifice.
375. The extremely dispassionate man alone has Samadhi, and the man of Samadhi alone gets steady realisation; the man who has realised the Truth is alone free from bondage, and the free soul only experiences eternal Bliss.
376. For the man of self-control I do not find any better instrument of happiness than dispassion, and if that is coupled with a highly pure realisation of the Self, it conduces to the suzerainty of absolute Independence; and since this is the gateway to the damsel of everlasting liberation, therefore for thy welfare, be dispassionate both internally and externally, and always fix thy mind on the eternal Self.
419. The result of dispassion is knowledge, that of Knowledge is withdrawal from sense-pleasures, which leads to the experience of the Bliss of the Self, whence follows Peace.
424. When the sense-objects excite no more desire, then is the culmination of dispassion. The extreme perfection of knowledge is the absence of any impulsion of the egoistic idea. And the limit of self-withdrawal is reached when the mind-functions that have been merged, appear no more.
373. It is only the dispassionate man who, being thoroughly grounded in Brahman, can give up the external attachment to the sense-objects and the internal attachment for egoism etc.
175. Attaining purity through a preponderance of discrimination and renunciation, the mind makes for Liberation. Hence the wise seeker after Liberation must first strengthen these two.
203. This realisation is attained by a perfect discrimination between the Self and the non-Self. Therefore one must strive for the discrimination between the individual soul and the eternal Self.
334. The dwelling on external objects will only intensify its fruits, viz. furthering evil propensities, which grow worse and worse. Knowing this through discrimination, one should avoid external objects and constantly apply oneself to meditation on the Atman.
160. The stupid man thinks he is the body, the book-learned man identifies himself with the mixture of body and soul, while the sage possessed of realisation due to discrimination looks upon the eternal Atman as his Self, and thinks, "I am Brahman".