Modulation, in music, means that the music changes key. A piece of music might, for example, be "in the key of C major" (meaning that it uses the notes of a C major scale, and the C sounds like the "home key" or "tonic" as it is called in music theory). Then it could modulate to G major so that the G now feels like the home key and the notes of a G major scale are used (the Fs will be F sharps).
Modulations like the one above are very common, because G is closely related to C (it is the 5th note in a C major scale: the "dominant"). A modulation to the subdominant (4th note of the scale) is also common (e.g. from C major to Fmajor). Music often modulates to the relative minor (e.g. C major to A minor).
A modulation that goes to a key whose tonic is not part of the original key is called a "chromatic modulation". Modulating from C major to A flat major would be a chromatic modulation because A flat is not a note in the C major scale.
Most pieces of music will modulate, especially if they are long pieces. It gives the music variety and helps to give it shape: the farther away from the tonic it goes the more tension there is. When the music eventually returns to the original key it feels like a homecoming.