Maxwells Equation in Time varying field
So the equation you have here is the Maxwell-Faraday law of induction, which calculates the induced emf caused by a time-changing magnetic flux through a conductor. This is more easily seen if you look at the integral form of the equation, since the negative line integral of an electric field gives the emf (induced voltage) and the surface integral of the B field gives flux (B field is flux density, so double integration gives flux).

The first case shown could be used to find the induced emf of a stationary coil within a time-varying magnetic field.

The second case could be used to find the induced emf of a moving coil in a time-invariant magnetic field.

The third case could be used to find the induced emf of a moving coil within a time-varying magnetic field.