“Man becomes conscious of himself and his humanity only in society and only by the collective action of the whole society.”

Variant translations:
A natural society, in the midst of which every man is born and outside of which he could never become a rational and free being, becomes humanized only in the measure that all men comprising it become, individually and collectively, free to an ever greater extent.
Note 1. To be personally free means for every man living in a social milieu not to surrender his thought or will to any authority but his own reason and his own understanding of justice; in a word, not to recognize any other truth but the one which he himself has arrived at, and not to submit to any other law but the one accepted by his own conscience. Such is the indispensable condition for the observance of human dignity, the incontestable right of man, the sign of his humanity.
To be free collectively means to live among free people and to be free by virtue of their freedom. As we have already pointed out, man cannot become a rational being, possessing a rational will, (and consequently he could not achieve individual freedom) apart from society and without its aid. Thus the freedom of everyone is the result of universal solidarity. But if we recognize this solidarity as the basis and condition of every individual freedom, it becomes evident that a man living among slaves, even in the capacity of their master, will necessarily become the slave of that state of slavery, and that only by emancipating himself from such slavery will he become free himself.
Thus, too, the freedom of all is essential to my freedom. And it follows that it would be fallacious to maintain that the freedom of all constitutes a limit for and a limitation upon my freedom, for that would be tantamount to the denial of such freedom. On the contrary, universal freedom represents the necessary affirmation and boundless expansion of individual freedom.
This passage was translated as Part III : The System of Anarchism , Ch. 13: Summation, Section VI, in The Political Philosophy of Bakunin : Scientific Anarchism (1953), compiled and edited by G. P. Maximoff
Man does not become man, nor does he achieve awareness or realization of his humanity, other than in society and in the collective movement of the whole society; he only shakes off the yoke of internal nature through collective or social labor... and without his material emancipation there can be no intellectual or moral emancipation for anyone... man in isolation can have no awareness of his liberty. Being free for man means being acknowledged, considered and treated as such by another man, and by all the men around him. Liberty is therefore a feature not of isolation but of interaction, not of exclusion but rather of connection... I myself am human and free only to the extent that I acknowledge the humanity and liberty of all my fellows... I am properly free when all the men and women about me are equally free. Far from being a limitation or a denial of my liberty, the liberty of another is its necessary condition and confirmation.
Man, Society, and Freedom (1871)
Context: The materialistic, realistic, and collectivist conception of freedom, as opposed to the idealistic, is this: Man becomes conscious of himself and his humanity only in society and only by the collective action of the whole society. He frees himself from the yoke of external nature only by collective and social labor, which alone can transform the earth into an abode favorable to the development of humanity. Without such material emancipation the intellectual and moral emancipation of the individual is impossible. He can emancipate himself from the yoke of his own nature, i. e. subordinate his instincts and the movements of his body to the conscious direction of his mind, the development of which is fostered only by education and training. But education and training are preeminently and exclusively social … hence the isolated individual cannot possibly become conscious of his freedom.
To be free … means to be acknowledged and treated as such by all his fellowmen. The liberty of every individual is only the reflection of his own humanity, or his human right through the conscience of all free men, his brothers and his equals.
I can feel free only in the presence of and in relationship with other men. In the presence of an inferior species of animal I am neither free nor a man, because this animal is incapable of conceiving and consequently recognizing my humanity. I am not myself free or human until or unless I recognize the freedom and humanity of all my fellowmen.
Only in respecting their human character do I respect my own....
I am truly free only when all human beings, men and women, are equally free. The freedom of other men, far from negating or limiting my freedom, is, on the contrary, its necessary premise and confirmation.