A counterpoint is something that contrasts, and to counterpoint is to provide a contrast. In music, counterpoint is when two separate melodies are played or sung at the same time.
When a composer writes a piece of music using voices that follow different rhythms or pitches but ultimately come together harmonically, she uses counterpoint. And if you're on the school debate time, you might offer a counterpoint to an opponents argument. You can also use this word as a verb to mean "to highlight difference:" "My tidy bookshelves counterpoint the mess of papers and books on my desk."