Heinrich events are massive glacier discharges from the ice sheets around the North Atlantic Ocean which occurred every 7,000-10,000 years during the last glacial period (10,000-50,000 years ago). Each of these events also triggered an abrupt atmospheric warming of some 10 degrees Celsius around the northern North Atlantic. The warming (Dansgaard-Oeschger event) occurred rapidly, in about twenty years, lasted a few hundred years, and terminated abruptly again, within a few decades. We suggest that such past rapid climate changes during the last glacial maximum have occurred due to rapid sea ice melting and formation. A specific mechanism is proposed for the climatic effects of Heinrich events. The synchronous iceberg discharges from several ice sheets around the North Atlantic are explained by a nonlinear phase locking between the different glaciers.