Do autopilots force the aircraft to fly over certain coordinates?
Over the North Atlantic, there are no predefined low-level or high-level airways as there are over the continents. In order for aircraft to get a tailwind for eastbound flights and get out of the wind for westbound flights, Canadian and UK air traffic control set tracks based on the expected wind conditions twice a day.

The lines you are seeing are called an 'Organized Track System'; is this part of the world, they're called 'NAT' (North Atlantic) Tracks. Five to six roughly-parallel tracks will be defined and move around every day, but they will generally go between whole degrees of latitude and 10° increments of longitude.

For example, tonight's (Dec 31/13) track BRAVO ('B') will go from a intersection in the UK called...

ERAKA (at 58°N/10°W) to
60°N/20°W to
61°N/30°W to
61°N/40°W to
60°N/50°W to
MOATT (at 58.025°N/59.928°W) to
LOMTA (at 57.203°N/62.619°W).