Generally, in mathematics, a canonical form is a function that is written in the most standard, conventional, and logical way. For example, polynomials are usually written with the terms in descending powers: it is more usual to write x2 + x + 30 than x + 30 + x2, although the two forms are essentially equivalent.
This word is used by theologians and canon lawyers to refer to the canons of the Eastern Orthodox and Roman Catholic churches, adopted by ecumenical councils.
Canonical can also mean "part of the canon", i.e., one of the books comprising the biblical canon, as opposed to apocryphal books.
Canonical variables are essential in the Hamiltonian formulation of physics, which is particularly important in quantum mechanics.