A canonical form assigns a distinguished representative to every equivalence class of mathematical objects. Two objects are equivalent precisely when they have the same canonical form, so canonical forms can be used to test equivalence.
For graphs, a canonical labeling is an ordering or renaming of the vertices that produces a distinguished labeled representative of a graph isomorphism class. That representative, rather than the labeling that produces it, is the canonical form of the graph.
In a positive geometry, the canonical form is the distinguished meromorphic top-degree differential form having only logarithmic singularities on the boundary, with residues equal to the canonical forms of the boundary pieces.
