Increasing current in a coil of wire will generate a counter emf which opposes the current. Applying the voltage law allows us to see the effect of this emf on the circuit equation. The fact that the emf always opposes the change in current is an example of Lenz's law.
The relation of this counter emf to the current is the origin of the concept of inductance. The inductance of a coil follows from Faraday's law.