Exposing a coil or loop to a changing magnetic flux will generate a current if the circuit is complete. The direction of the current is given by Lenz's Law:

Lenz's Law: A changing magnetic flux induces an emf that produces a current which sets up a magnetic field that tends to oppose whatever produced the change.

Coils and loops don't like to change, and they will try to counteract any changes in magnetic flux imposed on them. They are not successful - the change can be made, but the coil or loop tries to oppose the change while the change is taking place.

This tendency to oppose is why there is a minus sign in Faraday's Law.