What is charging current in transmission line?

In a transmission line, air acts as a dielectric medium between the conductors. When the voltage is applied across the sending end of the transmission line, current starts flowing between the conductors (due to imperfections of the dielectric medium). This current is called the charging current in the transmission line.

A transmission line has its own inductance and  mutual inductance, capacitance, these reactance will store power in its magnetic field when transmitting power.
Charging current is the current required by the line itself to charge (i.e. storing energy) in its own magnetic field.

Any two conductors separated by an insulating medium acts as capacitor . In case of overhead transmission lines, two conductors form the two plates of the capacitor and the air between the conductors behaves as dielectric medium. Thus an overhead transmission line can be assumed to have capacitance between the conductors throughout the length of the line.
In other words, we can say, the current associated with the capacitance of a line is known as the charging current.