The valedictorian is usually the student with the highest grades in a class. If the valedictorian of your class is someone you like and admire, you'll enjoy listening to her graduation speech.
At a high school or university graduation, the valedictorian traditionally gives a farewell speech, called a valedictory. This person is almost always the student in the class with the very best academic record. The origin of the word valedictorian is the Latin valedicere, which means bid farewell. Valedicere in turn comes from valere, be well, and dicere, to say.