A moduli problem $\mathcal{P}$ is a contravariant functor $\mathbf{Ell}\to\mathbf{Set}$. The objects of $\mathbf{Ell}$ are arrows $E\to S$ from an elliptic curve $E$ to a varying base scheme $S$. The morphisms are commutative squares $(E\to S)\to(E'\to S')$ in which the map $E\to E'$ is induced by an isomorphism $E\to E'\times_{S'}S$.
A moduli problem $\mathcal{P}$ is representable over $(\mathbf{Ell})$ if there exists an elliptic curve $\mathcal{E}\to \mathcal{M}(\mathcal{P})$ such that $\text{Hom}(-,\mathcal{E}\to \mathcal{M}(\mathcal{P}))\cong \mathcal{P}(-)$ is a natural equivalence of functors.
A moduli problem $\mathcal{P}$ is relatively representable over $(\mathbf{Ell})$ if for every $E\to S$, the functor on $\mathbf{Sch}_S$ defined by $T\mapsto \mathcal{P}(E\times_{S}T\to T)$ is representable by an $S$-scheme $\mathcal{P}_{E/S}$.
The book then remarks that every representable moduli problem is relatively representable. Namely, if $\mathcal{P}$ is a representable moduli problem, then for each $E\to S$ there is a natural isomorphism of the following $S$-schemes: $$ \mathcal{P}_{E/S}\to \text{Isom}_{S\times \mathcal{M}(\mathcal{P})}(\text{pr}_1^*(E),\text{pr}_2^*(\mathcal{E})) $$
But I'm confused by what $\text{Isom}_{S\times \mathcal{M}(\mathcal{P})}(\text{pr}_1^*(E),\text{pr}_2^*(\mathcal{E}))$ actually means. I can't figure out what the $\text{pr}_1$ and $\text{pr}_2$ maps are, but it seems to be pulling back along certain projection maps. If someone can briefly define for me what this object is, that would be awesome!