last of a dying breed= someone or something that is rare or nearly extinct. Can refer to humans or an endangered species. Example: The pigmy tribe found in the Amazon is the last of a dying breed. Some species of whales are the last of a dying breed due to whaling ships hunting them for whale meat. It can also mean someone who does something very few people do anymore . Example: The old people who do volunteer work once they retire, are the last of a dying breed. Which song in particular are you talking about?

It means the breed or type is dying out, and the person is the last.

It means the, among a group that's getting smaller ("the dying breed"), you/he/she/it is the last to stand ("the last of...").

it simply means that something is becoming less common. ^-^