I'm a newcomer to operads so apologies if this is a naive question.
The standard picture of an operad is of a collection of $n$-ary operations, thought of as objects with $n$ upward-pointing legs (inputs) and one downward-pointing leg (output), which can be composed in a sensible way. "Algebras over operads" then give rise to all sorts of algebras in the usual sense (associative, $A_\infty$ etc).
My understanding is that a PROP is basically the same thing but with operations allowed to have more than one output. Algebras over PROPs can also accommodate coproduct-like operations, and hence also include useful things like coalgebras and Hopf algebras.
Historically though, operads came later than PROPs. So why was it useful to single out the notion of an operad, as opposed to a general PROP?