Short answers, pulled from the story.
Georges Bataille was a French intellectual born on the 10th of September 1897 in Billom, Auvergne. He worked across philosophy, literature, sociology, anthropology, and art history, exploring eroticism, mysticism, surrealism, and transgression in essays, novels, and poetry. His work influenced post-structuralism and the thinking of Foucault, Derrida, and Lacan.
The accursed share is the excessive, non-recuperable portion of any economy that must be expended without gain. Bataille introduced the concept in La Part maudite, published in 1949 by Les Éditions de Minuit, arguing that surplus energy must either be spent luxuriously in art and spectacle or lost catastrophically in war. He called this excess expenditure 'dépense.'
Acéphale was a secret society founded by Bataille, its symbol a headless man. Every member agreed to serve as a potential sacrificial victim at the group's inauguration, but none would agree to act as executioner; an indemnity was offered but no executioner was found before the society dissolved shortly before the Second World War. Collaborators included André Masson, Pierre Klossowski, and Roger Caillois.
Bataille published Story of the Eye in 1928 under the pseudonym Lord Auch. 'Auch' is short for 'aux chiottes,' a French slang phrase meaning to dismiss someone to the toilet, making the name translate roughly as 'Lord to the shithouse.' The novel was initially read as pornography before later interpretation recognized its philosophical depth.
Bataille was shaped by his friendship with the Russian existentialist Lev Shestov, who introduced him to Nietzsche, Dostoevsky, and Plato. He also drew heavily from Hegel, Freud, Marx, Marcel Mauss, the Marquis de Sade, and Alexandre Kojève. Marcel Mauss's The Gift was crucial to Bataille's formulation of the accursed share.
Bataille's base materialism was a major influence on Derrida's deconstruction, and both thinkers used an unstable third term to destabilize philosophical oppositions. His influence is also significant for the phenomenological work of Jean-Luc Nancy, the social theory of Jean Baudrillard, and the psychoanalytic frameworks of Lacan and Julia Kristeva. He also founded the journal Critique.