Suppose we have a closed loop in a changing magnetic field. By Faraday's law this would induce an emf in the loop. However by the Kirchhoff's law the total emf around a closed loop is zero. It seems like we've reached a contradiction. What is going on here?
Kirchoff's Law is an approximation of Faraday's Law in the specific situation whereby the change in magnetic flux is negligible.
Kirchoff's Law means that voltages are like heights in gravitational potential; at every point in space, there is only one voltage, just like how at every point on the surface of the Earth, there is only one height of the land's surface.
Faraday's Law implies that Kirchoff's Law is wrong, and that there is a new contribution to voltages, confusing that it may be, that you can measure. Of course, for convenience, we will continue to define the scalar electric potential as if this new contribution does not exist, i.e. still has the nice property of having just one value anywhere in space, but there is a new contribution coming from the time derivative of the magnetic vector potential.