“The Great Seal was carefully designed by the founding fathers to symbolize the United States – to the world and to the future. It is America's symbolic mission statement, created by the people who gave us our freedom.” Read about meanings behind the symbols used in the Great Seal.
Source: GreatSeal.com

The Great Seal is included in the President’s seal.

Trivia: The Eagle’s head originally faced the talon that held the bundle of arrows, which symbolized “the power of war.”

However, in October of 1945, President Truman signed an Executive Order that said the eagle’s head should be turned to face the olive branch of peace to reflect America’s focus on peaceful resolutions to conflict.
Source: United States Department of State