When Rue of District 11 worked high up in the trees, and she saw the quitting time flag, she would use this four note song to tell her fellow harvesters when the working day was over. She would sing the tune into the trees and the surrounding mockingjays would pick up the song and sing it back to those on the ground.
In The Hunger Games movie, Rue sings the four notes to Katniss, who then whistles a different four-note melody back to Rue.
During the Victory Tour an old man whistles Rue's song to honor her. After the event, he was shot in the back of the head on the steps of the Justice Building, along with two other people, in front of the crowd. This was also a prearranged signal for District 11 to perform District 12's honorary salute.
Katniss' four note melody is quite simple, in concert pitch (C), it is, G - Bb - A - D.
Rue's four note melody is also quite simple, in concert pitch (C), it is, Db - F - Eb - Gb (or enharmonically, C# - E# - D# - F#)