There is the Canadian stroke, which Andy and Rob have described pretty well (and I concur, you need to be on the water to truly understand it).
Then there is also what we call Canadian Style paddling, sometimes also called "Omering" (after Omer Stringer). This is a solo paddling technique where you kneel in the center, or just abaft of center), with your knees tight into the bilge, heeling the canoe over. The heeling can be dramatic, often with the gunwales just off the water. A variety of strokes are used in various combination to manouver the canoe. Sue Plankis usually demonstrates this at Assembly and/or the Adk Freestyle Symposium recital.
It is similar to Freestyle, the main difference being that it wider canoes are usually used for Canadian Style, and most, if not all, the strokes are performed "on-side" where Freestyle uses both "on-side" and "off-side" strokes.
Both are often done with routines set to music, but knowing some of the manouvers that come out of Style and Freestyle paddling can enhance any paddling experience, especially river travel. Some refer to it as obedience lessons for your canoe, with the object of getting from here to there without hitting anything with as few strokes as possible.
Cheers,
Dan