In geophysics, an agonic line is an imaginary line drawn on a map connecting the points where the magnetic declination (the difference between true and magnetic north) is zero. Unlike the meridians of longitude that run directly from the north to south pole, the agonic lines can meander, reflecting variations in the Earth's magnetic field. Similarly, the agonic lines are not static; they can change position over the course of a year, requiring periodic mapping expeditions to confirm magnetic declination.
There is one agonic line running through each hemisphere. In the Western hemisphere, it runs roughly northwest to southeast, from the Great Lakes down through the Deep South. In the Eastern hemisphere, it runs down in the Pacific through an area called the Dragon Triangle. To the east of an agonic line, magnetic declination is west of true north. To the west of the line, the opposite is true. When navigating by compass, this declination needs to be accounted for in order for headings to be correct.
Sources:
http://www.trailsillustrated.com/skills/glossary.cfm
http://www.backpacker.com/jargon/0,2672,4,00.html