Answer: I can hardly improve on Willi Apel in his Harvard Dictionary of Music: a cadence is "A melodic or harmonic formula that occurs at the end of a composition, a section, or a phrase, conveying the impression of a momentary or permanent conclusion." The important part of Apel's definition is the reference to the "end of a composition... or phrase." Any piece of tonal music will have lots of places where the real or implied harmony would be a dominant chord (V) followed by a tonic chord (I or i) but that harmonic change is a cadence only if it's at the end of a musical phrase.

We'll need a few examples.

A very final sort of cadence is one that presents or at least implies in its melody the movement V-I or V-i (the chord built on the 5th or dominant degree of the scale, followed by the tonic chord). That's the authentic cadence. There's also the half cadence, which ends on the V chord and feels "unfinished." And there's the plagal cadence, also called the "amen" cadence, of IV - I. You could distinguish further subtypes of these, but mainly you need to be aware of the authentic, the half, and the plagal cadences.The following tune ought to be familiar (if not, it's in the traditional songs section of our Music Library). The first phrase ends with a half cadence:

And the next phrase has a more conclusive-sounding authentic cadence:

As for the plagal cadence, just think of "amen" - if you've ever been in a church you'll know that one. In the key of C you'd play the chord F (IV) and then I (C). The melody will usually move from F to E, the middle note of the C chord.