Chant du Cygne is French for "swan song". The phrase "swan song" is a reference to an ancient belief that the Mute Swan (Cygnus olor) is completely mute during its lifetime until the moment just before it dies, when it sings one beautiful song.
Mute Swans are not actually mute during life – they hiss – and they do not sing as they die.
By extension, "swan song" has become an idiom referring to a final theatrical or dramatic appearance, or any final work or accomplishment. It generally carries the connotation that the performer is aware that this is the last performance of his or her lifetime, and is expending everything in one magnificent final effort.