What's the difference between True vs Magnetic headings?
The "heading" refers to the direction an aircraft is pointing. For a Magnetic Heading, this is in relation to Magnetic North. For a True Heading, this is in relation to True North.
True North is directly over the earth's axis.
Magnetic North is somewhere over Canada, moving towards Russia.
To get the Magnetic Heading, you just read it off the magnetic compass.
To get the True Heading, you need to first read the magnetic compass, then either add an Easterly, or subtract a Westerly, magnetic variation; based upon the isogonic lines on your sectional (the purple dashed lines labeled 5°W, 3°E, etc).
Example 1: Magnetic Heading 177 w/ 3 degrees East Magnetic deviation = true course 180.
Example 2: Magnetic Heading 177 w/ 3 degrees West Magnetic deviation = true course 174.
Because of this, in the past, magnetic headings were used because a simple compass could be used. Finding reliable true headings was difficult until the era of things like the gyrocompass (patented in 1906 (Germany) and 1908 (USA)) and more recently, GPS.
You also need to take into account the compass deviation table which (hopefully) compensates for built-in magnetic influences.
Here's a question and answer what happens when you follow a constant magnetic heading due to compass deviation:http://aviation.stackexchange.com/questions/13248/klax-hdg-090%c2%b0-cross-the-atlantic-where-are-we-now/13249#13249
Note that gyrocompass only works when stationary or moving slowly, so while it existed in the early days of aviation, it couldn't be used on aircraft. Only with introduction of inertial navigation systems aircraft got gyroscopes good enough to align before departure and then maintain the true north with useful precision during the flight.