I believe that monads originated with Leibniz' metaphysical theory. Essentially, the monad acts as an interface between the worldly, corporeal and the spiritual, reflecting what happens on one side to the other and back.
Essentially an attempt to solve the mind-body problem.
As to why it was eventually snapped up in mathematical theor{y,ies} I do not know, but that is definitely what I think of when I hear "monad" (and monads in Haskell seem to share some of the qualities of Leibnizian monads).
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