What's a "canonical path"?
The whole point of making anything "canonical" is so that you can compare two things. For example, both ../../here/bar/x and ./test/../../bar/x may refer to the same location, but you can't do a textual comparison on the two paths. However, if you turn them into their canonical representation, they both become ../bar/x, and we see that they actually refer to the same thing.
In short, it is often the case that you have many ways of referring to one thing, and in that case you may be able to define a canonical representation which is unique and which allows you to get a handle on collections of such things.
(If you're looking for more examples, all of mathematics is full of "canonical" constructions for all sorts of objects, and very much with the same purpose in mind. Maybe this Wikipedia article can provide some additional directions.)
A good way to define a canonical path will be: the shortest absolute path (short, in the meaning of string-length).
This is an example of the difference between an absolute path and a canonical path:
absolute path: C:\abc\..\abc\file.txt
canonical path: C:\abc\file.txt
What a canonical path is (or its difference from an absolute path) is system dependent.
Typically if a (full) path contains aliases, shortcuts or symbolic links the canonical path resolves all these into the actual directories they refer.
Example: if /bin/a is a sym link, you can find it anywhere you request for an absolute path e.g. from java.io.File#getAbsolutePath while the real file (i.e. the actual target of the link) i.e. usr/local/bin/a would be return as a canonical path e.g. from java.io.File#getCanonicalPath