What you have here is a piece of a sentence because a sentence needs a subject and a verb. A subject is something or someone who is doing something or being something in the sentence. A verb is what the subject is doing or being.
Let's look at the following complete sentence:
The horse pranced.
The subject of that sentence is "The horse." It is is the horse that is going to do something. The verb is "pranced," which is what the horse was doing.
In your fragment, the subject is "the song, "John Brown's Body." So, what you need to make a complete sentence, at the very least, is a verb. Let's look at one possibility:
The song, "John Brown's Body" tells us a story about the Civil War.
The verb I have given the sentence is "tells," which is what the song is doing in the sentence.
You will notice that there is much more to follow the verb in this example because I have to let the reader know whom the song is telling something, and I have also explained what the song is tell us.
It is certainly possible to have a complete sentence with just a subject and verb, though. Here are a few examples:
All of those are sentences that I could add more to, of course, but each having a subject and verb, each meets the basic requirements for a sentence.