I classify this carol along with “Hark! The Herald Angels Sing” as having a very confusing title. In order to understand the meaning we’ll have to dive into a little grammar wonkery, with some biblical doctrine along the way.
Okay. Everybody got that? The lyrics were written by an American Unitarian Universalist minister, Edmund H. Sears, and, notably, they do not mention the actual birth of Christ at all. Let’s look at the first two lines of the carol itself:
It came upon a [or the] midnight clear,
That glorious song of old,