An operad is a monoid in the monoidal category of symmetric sequences equipped with the substitution product.
A module over an operad is just a right module over this monoid.
Right modules are very different from left modules, the latter are essentially algebras over an operad.
V. A. Smirnov?. ON THE COCHAIN COMPLEX OF TOPOLOGICAL SPACES. Mathematics of the USSR-Sbornik 43:1 (1982), 133–144. doi.
Martin Markl, Models for operads, Comm. Algebra 24 (1996), no. 4, 1471–1500. arXiv:hep-th/9411208v1.
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