When current $I$ in an inductor changes, the magnetic flux through the inductor also changes ($\Phi =LI$). This induces a 'back EMF' according to Faraday/Lenz: $E=-\frac{d\Phi }{dt}=-\frac{d(LI)}{dt}=-L\frac{dI}{dt}$ The negative sign indicates that the EMF opposes the change in current (it pushes back against increasing $I$ and tries to maintain decreasing $I$).