Quoted from Wikipedia, Lenz's Law states that "An induced electromotive force (emf) always gives rise to a current whose magnetic field opposes the original change in magnetic flux." In slightly simpler terms: nature abhors change and fights to oppose any change in magnetic flux by creating its own counter-current in the direction opposite the change (not that it is opposite the change, which may or may not be opposite the flux or magnetic field).
This can be demonstrated with an ammeter or galvanometer and a solenoid.
If a magnet is moved inside the solenoid, the flux changes, which induces a current in the solenoid.
If the magnet comes to rest inside the solenoid, then there is no change in flux, even though there clearly is both a magnetic flux and a magnetic field. Since there is no change in magnetic flux, there is no induced current.
