In his paper "On the Electrodynamics of Moving Bodies", Einstein defines synchronous clocks as clocks which satisfy $t_B-t_A=t'_A-t_B$. $A$ and $B$ are two points separated by empty space, and identical clocks are located at $A$ and $B$. A light signal is emitted from $A$ at time $t_A$ as measured by the clock at $A$. The signal arrives at $B$ at time $t_B$ as measured by the clock at $B$. The light signal is immediately reflected at $B$, and it returns to $A$ at time $t'_A$ as measured by the clock at $A$.
Why does he choose this definition for synchronous clocks? Why is this a sensible definition for synchronous clocks?
He does say this which might provide some insight into why he chose this definition: "We have not defined a common “time” for A and B, for the latter cannot be defined at all unless we establish by definition that the “time” required by light to travel from A to B equals the “time” it requires to travel from B to A."
I can't seem to understand this quotation, because I'm not sure what he means by "time" in this sense. So far time has only be defined at the locations of the two clocks, so you can't use one clock to measure the time for the light signal to move between the points, you would have to use a measurement from both clocks, but there is not necessarily any relation between the time displayed by the two clocks as far as I understand the situation.