What happens when current flows through inductor?

When current flows through an inductor, a magnetic field is created.

That's the simple explanation. More formally, an inductor is a magnetic device that reactively resists a change in current by presenting a voltage backwards towards the source. The equation for an inductor is ...

di/dt = v/L

... which means the the rate of change in current in amperes per second is proportional to voltage in volts and inversely proportional to inductance in henrys. Theoretically, this means that, if you place a constant voltage across an inductor, current will linearly increase without bounds to infinity. Practically, this will be limited by resistance and current capacity.