v is the sinusoidal voltage

i is the sinusoidal current due to voltage v

φ is the phase angle between v and i sinusoid

$$v=V_m\text{sin(ωt)}$$

$$i=I_m\text{sin(ωt + φ)}$$

The instantaneous power is given as $$p\mathrm{ \; =\; }v.i$$

$$p\mathrm{ \; =\; }{V}_m\text{sin(ωt)}.I_m\text{sin(ωt + φ)}$$

On simplification we get

$$p\mathrm{ \; =\; }\frac{V_m{I}_m}{2}\text{cos(φ)}-\frac{V_m{I}_m}{2}\text{cos(2ωt + φ)}$$

The first term is constant for a given load and the second term is a sinusoid of frequency 2ω

In one cycle the net value of the second term is zero. The first term is the average power

P is the average power and V & I are rms values

The average power is also known as real power.