When voltage is first applied across the two connections of an inductor, current starts to flow. Depending on the size of the inductor, this will slowly ramp up, as the magnetic field around the inductor builds. Once the field is fully built up, the current flow stabilizes at its maximum.
Unlike resistors, inductors show essentially zero impedance to direct current (save for the native resistance of the wire they are constructed from). To alternating current, their response depends on the frequency - low frequency signals can pass through an inductor, but not high frequency ones. The larger the inductor, the lower the frequencies which can pass through it.
Inductors are usually formed out of simple coils of wire; a core of magnetic material can be used to increase the inductance.