"cover band"

Does anyone know the significance of "cover" in the term "cover band"?

As per MW, an intransitive sense of cover is "to act as a substitute or replacement during an absence" as in:
"The substitute teacher covered my class while I was away on sabattical".

Many thanks to you, Bruce and Henry, for your quick replies. Finally(!), I now know why cover bands are so-called; the intransitive usage that you've pointed out makes perfect sense. Now I don't wish to come across as a nit-picking ingrate, Bruce, but in the illustrative example that you offered, I think that "cover" is being used transitively, with "class" as its direct object. However, one could say, "The substitute teacher covered for me while I was away".