I am reading Orbifolds as stacks?

Given Lie groupoids $\mathcal{G}$ and $\mathcal{H}$ there is a notion of what is called a bibundle from $\mathcal{G}$ to $\mathcal{H}$ which is supposed to be a ageneralized notion of a morphism of Lie groupoids.

(rough) Definition : A bibundle is a groupoid principal bundle which is equipped with a second groupoid action from the other side.

(precise) Definition : A bibundle from $\mathcal{G}$ to $\mathcal{H}$ is a manifold $P$ together with maps $a_L:P\rightarrow \mathcal{G}_0$ and $a_R:P\rightarrow \mathcal{H}_0$ such that

1. there is a left action of $\mathcal{G}$ on $P$ with respect to an anchor $a_L$ and a right action of $\mathcal{H}$ on $P$ with respect to an anchor $a_R$.

2. $a_L:P\rightarrow \mathcal{G}_0$ is a principal $H$-bundle.

3. $a_R$ is $\mathcal{G}$ invariant.

4. the actions of $\mathcal{G}$ and $\mathcal{H}$ commutes.

The point is to make collection of Lie groupoids as a $2$ category with Lie groupoids seen as objects, bibundles as morphisms between objects and isomorphisms of bibundles as maps between bibundles.

For that, we need to define what does it mean to say composition of two maps between Lie groupoids i.e., given bibundles $P:\mathcal{G}\rightarrow \mathcal{H}$ and $Q:\mathcal{H}\rightarrow \mathcal{K}$, we need to declare what is $P\circ Q:\mathcal{G}\rightarrow \mathcal{K}$.

We want it to be a bibundle. So, we need atleast maps $a_L:P\circ Q\rightarrow \mathcal{G}_0$ and $a_R:P\circ Q\rightarrow \mathcal{K}_0$.

What do we have is $a_L:P\rightarrow \mathcal{G}_0,a_R:P\rightarrow \mathcal{H}_0,a_L:Q\rightarrow \mathcal{H}_0,a_R:Q\rightarrow \mathcal{K}_0$ such that both $a_L$ are principal bundles.

(I do not know what is the motivation but) they have considered pullback $P\times_{\mathcal{H}_0}Q$ from maps $a_R:P\rightarrow \mathcal{H}_0,a_L:Q\rightarrow \mathcal{H}_0$. As $a_L$ is a submerison, $P\times_{\mathcal{H}_0}Q$ has a smooth manifold structure.

Then it says,

Since the action of $\mathcal{H}$ on $P$ is principal, the action of $\mathcal{H}$ on $P\times_{\mathcal{H}_0}Q$ given by $(p,q).h=(p.h,h^{-1}q)$ is free and proper. Hence the quotient $(P\times_{\mathcal{H}_0}Q)/\mathcal{H}$ is a manifold.

I am not able to understand what above statements mean. I have not come across the notion of quotient of a manifold by a Lie groupoid. I only know that if a Lie group acts properly, freely on a manifold, the quotient is a maniofld. What Lie group they are considering here? $\mathcal{H}_1$? I guess no, It is not even a group even though there is a smooth structure.

Can some one help me to see what I am missing here?