keel
The strip of wood running down the center of the outside bottom of the canoe is known as a keel. It provides some strength, some protection to the bottom, and some directional stability -- keeps the canoe going straight. It also makes the canoe harder to turn (the trade-off for directional stability), and makes it more likely that the canoe will hang up on shallow river or lake bottom, especially a rocky bottom.
A centerboard or dagger board is a completely different critter. A slot is cut through the center of the bottom of the canoe, a casing is built up around the slot to keep water out and to support the board, and a long (3-4 feet) narrow (typically 8 inches or more wide) is inserted through the casing to project below the hull. A centerboard may be hinged for easier raising and lowering; a dagger board is pulled completely out of the case to raise it. The purpose of both is to limit leeway -- to keep the canoe from blowing sideways when sailing with the wind coming from the side, rather than from the rear of the canoe.
Because of the increased turning effort and the slightly greater draft, many people dislike keels, especially those who canoe in shallow, rocky rivers with white water. Those who cruise mostly on lakes and quiet rivers may prefer to have a keel.
Some canoes have what is known as a shoe keel, which has a wide and thin section, rather than the section of a typical keel (such as the one on your canoe) which is roughly equal in width and height. A shoe keel provides some protection to the bottom, and some strength, while affecting handling less than a standard keel.
Those who dislike keels often remove them when recanvasing -- the loss of strength is usually not great enough to be concerned about.
Your canoe appears to have a keelson, an interior strip of wood which is structural (adds strength) down the center of the canoe; most canoes do not have a keelson.
Most sailing canoes use leeboards -- a pair of long narrow boards hung outside the boat to serve the same purpose as a a center board -- to limit leeway in a cross wind -- because the casing required for a center/dagger board gets in the way, and is a regular point of leakage, although some older sailing canoes, especially those built for racing, were built with centerboards.
If you remove the keel without recanvasing, you will have to figure out how to deal with the holes through the hull where the screws holding the keel on now pass.