The standard Lienard-Wiechert potentials describe the electromagnetic field at a point $P$ at time $t$ due to an arbitrarily moving charge $q$ at the retarded time $t-r/c$. An electromagnetic influence is assumed to travel, with the velocity of light $c$, from the moving charge $q$ at time $t-r/c$ to the field point $P$ at time $t$ while the charge moves along its path. This situation is illustrated on the left-hand side of the diagram. Physically the charge $q$ is in arbitrary motion whereas the field point $P$ is at rest in an inertial frame.
But the laws of electromagnetism are assumed to be time reversible. Therefore the time reverse of this process should occur in Nature. This is shown on the right-hand side of the diagram. Have I got this right? Basically all velocities are reversed including that of the electromagnetic influence.
Thus we have a picture in which an electromagnetic influence travels from a field point $P$ at time $t$ and intercepts a moving charged particle $q$ at a later time time $t+r/c$.
Note that I am not assuming that a signal goes backwards in time. I am "only" assuming that a physical process exists in which cause and effect are switched around in the temporal order. Instead of first moving charge then later field effect we have first field effect then later moving charge.
So to what physical situation does the advanced description correspond?
I believe that it might describe the situation in which the charge $q$ is at rest in an inertial frame and the point $P$ is in arbitrary motion. Thus, relative to an observer moving with point $P$, charge $q$ has an apparent motion illustrated by the right-hand diagram. The observer, at point $P$ and time $t$, measures a kind of inertial electromagnetic field that is determined by the apparent position of the charge at the advanced time $t+r/c$.
Could this be the answer to the meaning of the advanced solutions to Maxwell's equations?