The War Hawks tended to be from southern and western states, and were prompted by expansionist tendencies, in particular the desire to add Canada and Florida to the territory of the United States.
In December 1811 the U.S. Congress elected Henry Clay of Kentucky as speaker of the house, and Clay pushed the agenda of war against Britain.
President Madison was eventually convinced to go along with the demands of the War Hawks, and the vote to go to war with Britain passed by a relatively small margin in the U.S. Congress.
The resulting War of 1812 was costly to the United States, and at one point British troops marched on Washington, D.C. and burned the White House and the Capitol. And the expansionist goals of the War Hawks were not achieved.
The term "hawk" to describe someone who is in favor of beginning a war persists in American speech to the present day.