Here is an example which I like to have a name for. 

Let $P$ be a compact smooth manifold of dimension $p$, possibly with non-empty boundary.

Define $E(k,P)$ to be the space of smooth (codimension zero) embeddings
$$
\coprod_{k} D^p  \to P \, ,
$$
that is the space of embeddings of $k$ disjoint $p$-disks in $P$, where the image of each such embedding lies in the interior.

In particular, when $P = D^p$, the spaces $\{E(k,D^p)\}_{k\ge 0}$ form an operad. 

There is an evident "action" map
$$
E(\ell,P) \times (E(k_1,D^p) \times \cdots \times E(k_\ell,D^p)) \to 
E(k_1 + \cdots +k_\ell,P)
$$
given by insertion.

**Question:** What is this action an example of? (Does it have a name?)