Meaning of the word 'canonical' in physics

Even in physics, the term canonical requires a disambiguation for clarity. In the contexts you were citing, it means that it is a more general form. E.g. if you are dealing with momentum, then the canonical momentum refers to $p = p + q \bf{A}$, however, momentum in a Newtonian physics course would most certainly refer to $p=mv$, thus, a professor might call momentum canonical to clarify that he does not mean the more simple version, but the more general version.

For other uses of canonical, see Wikipedia's disambiguation below:

Hope this clears up your answer!