Watt is the unit of power. So, whenever power is absorbed by an element it is measured in Watts.
So, for example, when a current flows through a Resistor, the Power is dissipated as heat. So, when current flows through a resistive element some power is dissipated, measured in Watts.
So, Now, as you might expect, Watt-less current is the current which doesn't dissipate any power. How, is that possible you ask, lets see how.
The Power in an AC Circuit is given by the following relation. P = V.I.Cos(Ø)
Ø, being the phase angle between Applied voltage and the Alternating Current.
The Quantity Cos(Ø) is also called as Power Factor.
The Phase angle, Ø, is zero for Resistors.