Michael Faraday discovered that whenever a conductor is moved through
a magnetic field, or whenever the magnetic field near a conductor
is changed, currents flow in the conductor.
This effect is called
electromagnetic induction.
He performed literally hundreds of different experiments, each with its own
peculiarities, and made the amazing discovery that all of them could be described
by a single simple law, which we call it Faraday's law.
This law gives the magnitude and direction of the emf produced in a conducting
loop whenever the loop is moved, or whenever the magnetic field near the loop is
changed:
In this equation 
is the magnetic flux through the loop,
Since our physical interpretation of flux is that it counts the number of field lines that pass through an area, this law says that if the number of field lines through a loop is changed by any means, then an emf will be induced in the loop. The minus sign in Faraday's law indicates the direction of the induced currents, but its use requires so many complicated rules and negative signs that we usually get the direction of current flow from Lenz's law.