Bid'ah is innovation in religion, a belief or practice introduced after the formative period without warrant in the Qur'an, the sunna, or the practice of the earliest generations. The proof text is the report that "every innovation is misguidance, and every misguidance is in the Fire", and no one in the tradition disputes that some innovations are condemned. The whole argument is about how far the category reaches.
One position, associated with Salafi scholarship and with much of the Hanbali tradition, holds that in matters of worship the category admits no good kind: acts of devotion require positive evidence, so anything introduced into worship without it is misguidance, while worldly affairs are governed by a presumption of permission. On this reading the term does real work, and is applied to practices such as celebrating the Prophet's birthday, collective supplication after prayer, and the veneration of graves.
The opposing position, developed by al-Izz ibn Abd al-Salam and al-Nawawi and traced to a saying attributed to al-Shafi'i, divides innovation according to the five legal rulings: there is obligatory, recommended, permitted, disliked and forbidden innovation. Its standard examples of praiseworthy innovation are the collection of the Qur'an into a single codex, the systematic recording of hadith, the development of grammar and law as disciplines, and the building of schools, none of which the Prophet instituted, and all of which the first position must also account for.
Both sides cite the same remark. Umar ibn al-Khattab, seeing the Ramadan night prayer organised in congregation, is reported to have said "what an excellent innovation this is." The second position reads that as explicit licence; the first replies that what Umar restored had prophetic precedent and had lapsed only for fear of its becoming obligatory, so the word in his mouth is lexical rather than legal. Twelver Shia scholarship enters the argument from another direction, applying the charge of innovation to what it regards as post-prophetic departures by the majority, while defending as legitimate the mourning observances for Husayn that others call innovation. The label, in short, is one that every party uses and no party accepts.