Tonic and subdominant in C Play (help·info). C major and F major chords.
Subdominant (IV) in IV-V-I progression, in C Play (help·info)
In music, the subdominant is the technical name for the fourth tonal degree of the diatonic scale. It is so called because it is the same distance "below" the tonic as the dominant is above the tonic - in other words, the tonic is the dominant of the subdominant. It is also the note immediately "below" the dominant. In the C major scale (white keys on a piano, starting on C), the subdominant is the note F; and the subdominant chord uses the notes F, A, and C. In music theory, the subdominant chord is symbolized by the Roman numeral IV if it is within the major mode (because it is a major triad, for example F-A-C in C major) or iv if it is within the minor mode (because it is a minor triad, for example F-A♭-C in C minor).
In very much conventionally tonal music, harmonic analysis will reveal a broad prevalence of the primary (often triadic) harmonies: tonic, dominant, and subdominant (i.e., I and its chief auxiliaries a 5th removed), and especially the first two of these.
Subdominant (IV) in I-IV-I progression, in C Play (help·info)
A cadential subdominant chord followed by a tonic chord (the chord of the key of the piece) produces the so-called "plagal" (or "Amen") cadence.
"Subdominant" also refers to a relationship of musical keys. For example, relative to the key of C major, the key of F major is the subdominant. Music which modulates (changes key) often modulates into the subdominant when the leading tone is lowered by a half step to the subtonic (B to B♭ in the key of C). Modulation into the subdominant key often creates a sense of musical relaxation; as opposed to modulation into dominant (fifth note of the scale), which increases tension.
In sonata form, the subdominant key plays a subordinate though still crucial role: typically, in the recapitulation, there is a section written in the subdominant key, occurring at the point corresponding to the location in the exposition where the music modulated into the dominant key. The use of the subdominant in this location often serves as a way of keeping the rest of recapitulation in the tonic.