Answer: The "perfect fifth" is the strongest interval in music, next to the octave. Two chords whose roots are separated by a perfect fifth have a close relationship. The tonic note of every scale has two such closely related triads: the one a fifth above the tonic is the dominant triad, and the one a fifth below is the subdominant.

So every tonic tone is the center of a trio of strongly related chords, for example, F...C...G, where C is the tonic, G the dominant, F the subdominant.

A dominant chord must be major, so that its middle tone is a half step away from the root of its partner triad and can "lead" back to the tonic. It's the 'leading tone." In the key of C, the leading tone is B, which is the middle tone of the G major chord.

The subdominant is the reverse: the tonic chord is a fifth above the subdominant and if the tonic is major it has just the same relationship to the subdominant as the dominant has to the tonic.

The leading effect of a dominant can be further enhanced by adding a minor seventh to the major triad. That's like adding another leading tone, this one seeming like it wants to move to the middle tone of the tonic triad. For example, G-B-D-F sets up a strong sense of movement to C-E-F. That's called a "dominant seventh chord."

In every key there is just one dominant seventh chord that can be spelled using the notes naturally available in the scale. In major keys it's the chord built on the dominant tone, a fifth above the tonic. You can alter other chords, though, to make them sound like a dominant. In C major you could change the normal d minor chord to major and it will start to sound like the dominant of G, a fifth below D. Add a seventh, making D-F#-A-C, and the effect is even stronger. That's a "secondary dominant" - a dominant chord made by altering notes in a chord that is not ordinarily a dominant. This can be used to modulate to another key, or just to give a particularly strong sense of movement, as in the progression C major, a minor, D dom7, G dom7, C major.

Dominant triads are also discussed on pages 54-55 of Exploring Theory with Practica Musica.