A difficult, prestigious math competition for the students with the top AMC + AIME schools in the United States. Simply qualifying for the exam means that you're among the best in the nation.
Thomas Jefferson of Science and Technology has more USAMO qualifiers than any other school in the United States.
United States of America Mathematical Olympiad. It's a contest for the top 200 or so high school mathematicians in the country.
Only geniuses can qualify to take the USAMO, never mind win it.