If $\phi$ is a quantum field there's a simple interpretation of $$\langle 0 | T \phi(x) \phi(y) | 0 \rangle.$$ This quantity is simply the amplitude to propagate from $y$ to $x$. Diagrammatically, we can compute it by summing all Feynman diagrams with one $\phi$ field at $x$ and one $\phi$ field at $y$.
Now let $j^\mu$ be a conserved current, such as the electromagnetic current in QED. Occasionally, we compute correlators of the form $$\langle 0 | T j^\mu(x) j^\nu(y) |0 \rangle.$$ Is there a simple, possibly diagrammatic interpretation of such a correlation function? How about for a general current in a more complicated theory? How about for $n$ currents?
I know that you can just say what I said in my first paragraph with $\phi$ replaced with $j^\mu$, but I'm looking for something in terms of the fundamental fields.