Inductance is what opposes change in current in a circuit. In electronics the letter L represents inductance.
Inductors are devices which oppose any change in current regardless in what direction.
If you put a core inside, that's something that the coil is wound around all the time, like a pencil or a nail, that is exactly what a core is. So, as the current flows through the circuit, a magnetic field will induce in the coil. This field will start from 0 and then will expand to it's fullest value or flux density. As this flux field moves outward, it cuts across the wires that make up the core or otherwise called windings of the coil. As it opposes the source voltage it will also oppose the rise in AMPS or current and kinda act as a resistor at the same time.