Harmonic current refers to the current used in musical applications. It's used to produce harmonies through instruments such as electric guitars, pianos, etc.

Without it, all music would sound flat.

An offline flyback power converter employing coupled primary transformer windings to achieve input harmonic current correction is introduced. By controlling the turn-ratio of the windings

I don't think this question has any thing to do with music. Remember this is an electrical engineering forum. Check http://www.ce-g.com/99ARG/Martin103.html and Harmonic Current

Harmonic Current is multiples of the fundamental current. As in a fundemental of 60 Hz would have harmonics of 120 Hz, 180 Hz, 240 Hz, 300 Hz etc. You see that the 60 is multipled by integers of 1,2,3,4,5 etc. In the real world, the even harmonics cancel out, and you are left with 180, 300, 420, etc. (3,5,7). Hope that answers your question