Answer: The American Ideals that are most represented by celebrating the life and dreams of Dr. Martin Luther King Jr. (also MLK Jr.) are equality for all and the use of nonviolent means of protest to move progressive ideas from dream to reality.
Dr. King used his life to inspire others to help move the Civil Rights movement in a positive direction and affect real change. The early part of the 20th century was still a very difficult time for African-Americans in the United States. There were still horrible events that occurred in the U.S., especially in the South, like lynchings - hanging people, specifically African-Americans as a form of local justice without due process or a court of law.
Dr. King was assassinated (or killed) in 1968. Dr. King represented freedom and equality to millions of Americans. The Civil Rights Movement in America continued forward and much social progress with regards to freedom and equality due to Dr. King's ideals and leadership during the 1950s and 1960s.
These ideals continue to be celebrated every MLK Jr. day, a day that his heirs have promoted as a part of social campaign to give back to local communities, not a day off of work or school, but a day to give back.