Short answers, pulled from the story.
The Apple of Discord was a golden apple thrown by Eris, the goddess of strife, at the wedding of Peleus and Thetis. Eris was not invited to the wedding and threw the apple in anger to ruin the gathering. The apple sparked a dispute among Hera, Athena, and Aphrodite that led to the Judgement of Paris and, ultimately, the Trojan War.
In some later sources, Eris inscribed the apple with a phrase meaning "for the fairest" or "to the most beautiful." The most widely cited Greek form is transliterated as tē(i) kallistē(i), and the Latin equivalent is formosissima. The inscription named no recipient, which was what made it a trigger for conflict among the three goddesses.
Ptolemaeus Chennus proposed a rationalized version of the myth in which no apple was involved. He wrote that Hera, Athena, and Aphrodite instead disputed over which would receive a priest named Melus as her own, with Melus meaning "apple" in Greek. In his version, Paris still decided the contest in favor of Aphrodite.
In common parlance, "apple of discord" refers to the core or crux of an argument, or a small matter that grows into a larger dispute. The phrase describes a seemingly minor trigger that turns out to carry serious consequences.
La manzana de la discordia is a city block in the Eixample district of Barcelona, Spain. It was named after the Apple of Discord because the Spanish word manzana means both "apple" and "city block." The block features four competing interpretations of Modernisme architecture by Antoni Gaudí, Lluís Domènech i Montaner, Josep Puig i Cadafalch, and Enric Sagnier.
The Block of Discord in Barcelona's Eixample district features Casa Batlló by Antoni Gaudí, Casa Lleó Morera by Lluís Domènech i Montaner, Casa Amatller by Josep Puig i Cadafalch, and Casa Mulleras by Enric Sagnier. Each building represents a different interpretation of Modernisme architecture.