Magnetic heading is your direction relative to magnetic north, read from your magnetic compass. True heading is your direction relative to true north, or the geographic north pole. The difference is due to the magnetic north pole and geographic north pole being hundreds of miles apart.
The Earth rotates about its geographic axis; maps and charts are drawn using meridians of longitude that pass through the geographic poles. Directions measured from the geographic poles are called true directions.
The magnetic North Pole to which the magnetic compass points is not collocated with the geographic North Pole. Directions measured from the magnetic poles are called magnetic directions.
All ATC instructions are sent using the magnetic heading.
References: Chapter 8 of the Pilots Handbook of Aeronautical Knowledge