Shirk is the association of partners, rivals or equals with God, and it is the exact negation of tawhid. The Qur'an treats it as the one thing not forgiven in those who die unrepentant of it: "God does not forgive that partners be associated with Him, but He forgives what is less than that for whom He wills" (4:48, repeated at 4:116). Classical theology divides it into major shirk, directing worship, ultimate trust or ultimate fear to another, and minor or hidden shirk, of which the standard example is riya, performing acts of worship to be seen doing them.
The Qur'an's primary referent is the deities of pre-Islamic Mecca, the "partners" whose intercession its opponents claimed (39:3). It extends the charge to taking rabbis and monks as lords beside God (9:31), and it addresses Christian formulations in terms its own readers took as a warning against compromising divine unity (4:171, 5:73). Christian theologians dispute that reading, holding trinitarian doctrine to be monotheistic; the disagreement is old and is one of the fixed points of Muslim-Christian theological exchange.
Within Islam the argument is over reach. Ibn Taymiyya, and later Wahhabi and Salafi scholarship, extended shirk to intercession sought at tombs, vows made to saints and oaths sworn by other than God. Sufis, most traditionalist Sunnis and Shia reject the extension, holding that asking a righteous person to pray for one no more makes that person a god than asking a living friend to do so. Mainstream jurists of every school have hedged takfir, pronouncing another Muslim an unbeliever, with heavy restrictions, precisely because the charge of shirk is so grave.