"Classical field configuration" - QFT I often encounter the term "classical field configuration" in the scope of QFT, but I have a hard time interpreting what it really means.
If I understood it correctly, then a general field configuration is just an explicit form of a field, e.g. a free field $\phi(x)$. If this is correct, then I wonder what a classical configuration is exactly!
 A: A classical field configuration of a field $\phi(x)$ is just an explicit form for $\phi(x)$ that satisfies the equations of motion.
This is in contrast to quantum fields, where $\phi(x)$ is an operator-valued distribution. Instead of thinking of the field as a single function, we want to know the probability amplitude for the field to be in a given configuration. You can characterize the distribution by looking at moments, such as $\langle \phi(x)\rangle$, $\langle \phi(x) \phi(y) \rangle$, $\langle \phi(x) \phi(y) \phi(z)\rangle$, etc, where the average is taken in a given state (typically the vacuum state, especially in introductions to QFT). Much of the formalism of quantum field theory is devoted to ways to compute these correlation functions, sometimes also called Green's functions.
NOTE I removed a parenthetical statement "(note that there is a non-zero probability amplitude for the field to be in configurations that don't satisfy the classical equations of motion)" because, upon reflection, I don't know what I meant by that. In the path integral formulation, you do sum over field configurations that do not satisfy the classical equations of motion. In the operator language, general correlation functions do not evolve according to the classical equations of motion because of contact terms; see Eq 2.13.9 of https://sites.krieger.jhu.edu/jared-kaplan/files/2016/05/QFTNotes.pdf. Thanks to user @AlexGower for discussions on this point.
