What is the real meaning of phase. I had a problem while deriving phase relationship between e.m.f and current. Please tell me practical meaning of phase with an easy example.

I will be highly obliged.

We know that an alternating emf can be represented by  where E is the instantaneous value, E₀ is the peak value and ωt is the phase angle.The variation of emf is sinusoidal. 

Phase of an oscillating particle tells us about  the position of the particle from the equilibrium position at any instant. Phase of an alternating current or voltage gives the fraction of the time period that has elapsed(ωt =2πt/ T) since ac or voltage last passed its zero value in the positive direction.

1.Consider the following figure. It shows two waves which are in the same phase. Two waves are in same phase means that they both are zero at the same instant  and both pass through their maximum value at the same instant. and always have similar time reletionships. 

 

In the above figure one wave form represent an alternating emf and other represents an alternating current. Both waves are in the same phase . Hence we can say that emf is in phase with the current.

2. Consider the following figure showing two waves that are out of phase.

 

Here the two waves are 90° out of phase. i.e. the two sinusoidal waves forms differ in phase by 90°(π/2). The voltage curve reaches zero at an instant when the current curve pass through maximum value.