Usually, by a complex of $R$-modules, where $R$ is a ring (or sheaf of rings), one means a sequences of $R$-modules $C_n$ and $R$-homomorphisms $d_n:C_n\to C_{n-1}$ such that $d_{n-1}\circ d_{n}=0$.
However, consider the de Rham complex $$ \mathcal{O}\to\Omega^1\to\cdots\to\Omega^n $$ where each term is an $\mathcal{O}$-module and each differential is merely $\mathbb{C}$-linear. I have seen thousands of times that the de Rham complex is a complex of right $D$-modules. ($D$ is the sheaf of differential operators)
What does “complex of right $D$-modules” means here?