Canonical VS Graph Isomorphism
this might take a few iterations, but perhaps it can be moved to chat if it gets too long.  are you wondering about a specific application or just the general concept?  as far as i know, the canonical form of something is the unique/simplest arrangement/representation of that something.  as for isomorphism (one to one relationship, a function gets you from one set to the other), you can oversimplify it and think about factors of numbers.

for a moment consider an analogy - instead of graphs, using sets of numbers.  this is randomly off the top of my head so hopefully there aren't too many holes in it.  we have

$A = 6, 10, 14$

and

$B = 18, 30, 42$

let's call $A$ and $B$ isomorphic because to get between any value in $A$ to the corresponding value in $B$, you multiply or divide by 3.  now let's introduce another isomorphic set:

$C = 3, 5, 7$

it looks like $A$, $B$, and $C$ are all isomorphic because there is a one to one relationship between any of their initial values.  the same can be said for any of their middle values, or any of their ending values.  while it's great that they're all isomorphic, we'll consider something additional about $C$.  i'm going to call $C$ canonical because if you remove the greatest common factor from $A$, or you remove the greatest common factor from $B$, you get $C$.  there is no common factor we can remove to reduce $C$ itself.

extending this, you can see that a canonical representation of a graph is an isomorphic version of that graph, but not necessarily the other way around.  all isomorphic versions of said graph will reduce to the same canonical form.

EDIT:

that being said, the definition of canonical is more complicated for graphs.  first, for graph isomorphism, this page about a code named bliss presents some small graphs as an example.  they define $G_{1}$ as


and $G_{2}$ as


and offer two transformations for $G_{1}$ that will make $G_{1}$ and $G_{2}$ isomorphic.  first, they consider $\{\langle 1\to 2, 2\to 4, 3\to 1, 4\to 3\rangle\}$, and then $\{\langle 1\to 2, 2\to 4, 3\to 3, 4\to 1\rangle\}$ - both of these transformations swap vertices.  the transformations result in the following isomorphic graphs:



each pair of connected vertices has a corresponding pair in $G_{2}$ ($2\to 1,3,4; 1\to 4; 3\to 4$).

now, to discuss canonical graphs, we must identify a cost function with which we can measure what is the 'most canonical' form.  this paper mentions metrics such as area, minimum angle, and total number of bends.  for simplicity, i'll try to minimize bends and favor angles that are closer to $90^{\circ}$.

if you use a coordinate transformation, you can see that this simple graph



and this graph



are isomorphic.  the same edges connect the same pairs of vertices, and if you move vertices from one around, you can make the other.  this graph



is also isomorphic with the first two, but since it has the optimal amount of bent edges (zero) and optimal angles (four right angles), it is also the canonical representation for these graphs.

for further reading, you might consider this paper, which discusses several algorithms used to find canonical representations for web mining, or this paper, which discusses canonical representations of binary decision diagrams, word-level decision diagrams, binary moment diagrams, taylor expansion diagrams, and finite field decision diagrams.  

tl;dr:

just have a look at the minion with bananas on slide 10 of this presentation.