1) To warn European Powers not to get involved with the affairs of the Western Hemisphere. That the Western Hemisphere would not further be colonized by Europeans, and the U.S. would leave existing Colonies alone; not involved in their International affairs or wars.
2) President James Monroe wanted to make sure that Europe did not take Spain's colonies, as many were on the verge of their own independence. Prussia, Austria, and Russia had formed the Holy Alliance with the goal of defending monarchical government. It was a precaution really.
3) The United States was prosperous, as we no longer had to worry about wars, we could focus on trade to gain a better economy. Also the Europeans benefited from the fact that they could not stand another war and win, due to previous wars which had left them disorganized and slowly building back the economy.
hope this helps