Dominant
The dominant is the fifth degree of the scale and the triad built on it, marked V (or D). In C major it is G, and the chord G: G–B–D. The dominant pulls back towards the tonic.
The dominant stands a fifth above the tonic: C–G. It is the most tense of the three main chords. It contains the seventh degree of the scale, B, which is left hanging and strains a half step up to C. That is why, after the dominant, the ear expects the tonic.
Add a fourth note, F, and the dominant becomes the dominant seventh V7: G–B–D–F, G7 in chord letters. The pull is even stronger: F falls to E, B rises to C. A cadence in which V or V7 returns to I sounds finished; stopping on V sounds like a question.
In other keys the dominant is still the fifth degree: D (the chord D) in G major, C (the chord C) in F major, E in A minor. In the progression I–IV–V–I the dominant is the furthest point before coming home. To keep the hand still, G is often played in the inversion B–D–G.
What it sounds like
The dominant sounds tense and expectant, like a breath taken before the end of a sentence. When the tonic follows, the tension lets go.
Where it is taught: the studio’s interactive textbook, chapter 9, “Triads: C, F, G” and chapter 11, “Triad inversions and the dominant seventh”.