An apple of discord is a reference to the Golden Apple of Discord (Greek: μῆλον τῆς Ἔριδος) which, according to Greek mythology, the goddess Eris (Gr. Ἔρις, "Strife") tossed in the midst of the feast of the gods at the wedding of Peleus and Thetis as a prize of beauty, thus sparking a vanity-fueled dispute among Hera, Athena, and Aphrodite that eventually led to the Trojan War (for the complete story, see The Judgement of Paris). Thus, "apple of discord" is used to signify the core, kernel, or crux of an argument, or a small matter that could lead to a bigger dispute.
Because of this, the Roman goddess corresponding to the Greek Eris was named "Discordia". Also, in German and in Dutch, the words are used a lot more often colloquially than in English, though in German the colloquial form is not Apfel der Zwietracht (lit. "Apple of Discord") but Zankapfel ("Quarrel-apple") and rarely Erisapfel; the Dutch is twistappel ("Strife-apple").
In the Eixample district of Barcelona, there is a block nicknamed in Spanish La manzana de la discordia (Catalan: L'illa de la discòrdia). The reason for this usage is that manzana means both "apple" and "city block" in Spanish. It was so named ("block of discord") because it features four different interpretations of Modernisme architecture: Antoni Gaudí's Casa Batlló, Lluís Domènech i Montaner's Casa Lleó Morera, Josep Puig i Cadafalch's Casa Amatller, and Enric Sagnier's Casa Mulleras.
In some later sources, Eris inscribed on the apple "for the fair" or "to the most beautiful" before tossing it. The most popular version of the inscription is ΤΗΙ ΚΑΛΛΙΣΤΗΙ (Ancient Greek: τῇ καλλίστῃ, romanized: tē(i) kallistē(i), Modern Greek: τη καλλίστη ti kallisti; "for/to the most beautiful"). Καλλίστῃ is the dative singular of the feminine superlative of καλός, beautiful. In Latin sources, the word is formosissima.