what is a “senior concert”? A high school senior concert?

This appears to be references to what are important events to Americans in high school. The highest grade in an American high school, the 12th grade, is known as the senior class. So a senior concert would be a concert put on by members of the senior class (i've never heard of a senior concert, but that's hardly conclusive). When one completes the high school requirements, when one graduates, there is a graduation ceremony at which family members attend, it is an important ritual event. Prom is a shortening of promenade, and it refers to another big event in the life of a high school student, a formal dance. The students attending wear formal clothing, and a girl's prom dress is very important to her. Usually, there is a junior prom, put on by the members of the junior class, the 11th grade students; and there is a senior prom, put on by the senior class. "The Prom" refers to the senior prom, and is usually considered the most important social event of the year.