What does the negative sign indicate in Lenz’s Law?

Hint: Lenz’s law of electromagnetic induction states that the current induced in a wire due to change in the amount of magnetic flux passing through it is in a direction such that it tries to oppose the change in flux causing that current.

Complete Answer:
When a conductor is kept in a magnetic field, a net magnetic flux passes through the area enclosed by the loop formed by that conductor. If the net flux passing through the conductor changes, a net electromotive force is induced in the conductor and current flows through it.
It is known that when current flows through a conductor, it creates a magnetic field around it. So, this current that flows due to the induced emf also creates a magnetic field around it. Then, according to Lenz’s law, this current has a particular direction, such that the magnetic field produced by the current in the conductor is opposite to that of the magnetic field that has a changing flux. This behaviour of the conductor is similar to Newton’s third law involving action and reaction.
When the flux in conductor changes, it tries to oppose this change of flux by inducing a current in such a way that it creates a mechanical repulsion that is observable between two same poles of a magnet.
Therefore, it can be said that the direction of the magnetic field produced by the conductor is opposite to the direction of the magnetic field of the source magnet.
This opposition in change and the opposite direction is represented by putting a minus sign before the rate of change of flux in the equation-
 $ \varepsilon = - \dfrac{{d\phi }}{{dt}} $
Where $ \varepsilon $ is the induced emf.
 $ \dfrac{{d\phi }}{{dt}} $ is the rate of change of magnetic flux.

Note:
Lenz law is similar to Faraday’s law, but not the same. Faraday’s law gives the magnitude of the emf induced in the conductor by changing magnetic flux, while the Lenz law gives the direction of this induced emf.