Why in inductor the current lags the voltage?

Because in an AC circuit, a capacitor opposes the change of voltage in at. At the peak of the voltage waveform, there is no change (it is nearly flat), so at this same point in time, the current waveform is at zero.

Likewise, when the voltage waveform crosses zero, it is changing at its fastest rate, so the current is at its peak.

If you draw these two waveforms next to one another, you will see the voltage has the appearance of being behind the current - hence the term 'lag'.