An inductor is like a small solenoid in a circuit. It behaves like any loop of wire with currents, and follows the rules of em induction, such as Lenz's law. Conceptually, inductors resist changes in magnetic flux. This means they fight batteries when first connected, and therefore prevent current from flowing initially, and after a long time become nothing more than wires in a circuit, with steady current flowing.
The voltage across an inductor was derived from Faraday's law to be V = -L di/dt. Inductors with current flowing around the loops of wire also has a B-field in the tube, and this field stores energy, U = (1/2)Li^2. Check out this video to see how to do the mathematical derivations of current as a function of time when inductors are in series with a resistor.
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