What role does a countersubject play in a fugue?

In a fugue, a countersubject serves as a secondary melodic line or voice that accompanies the main subject when it is stated in another voice.12

While the subject is often accompanied by counterpoint, the term "countersubject" is specifically reserved for instances where this accompanying melodic pairing systematically recurs throughout the piece. Because the countersubject must function effectively regardless of whether it is positioned above or below the subject, the relationship between the two must be invertible.1

It is important to note that not all fugues utilize a countersubject; in many compositions, the counterpoint accompanying the subject is free and does not recur in a systematic way.1