The music you are listening to comes from the 12th Century. There are several voices singing in harmony. This is when two or more voices sing at a different pitch and still make a pleasing sound. Not all Medieval music was sung in parts like this. In churches and monasteries, for example, monks or nuns sang psalms and hymns in chorus, all singing the same notes.
This was called plain-song. The tunes they used were called Gregorian chant, because it was Pope Gregory (590-604 AD) who put together a great book of hymn tunes and sent singing teachers to every church and monastery in Europe to make sure the same tunes were used everywhere.
During the Middle Ages, music gradually became more complicated. The singers in a choir might sing the same tune, but at different pitches. Or a choir could be split into sections, one group singing the main tune, others singing variations on the same tune but quicker and higher or lower than the main tune, weaving in and out of it. In those days written music looked like this (right)
Music for a troubadour song >>
These notes were called 'neumes'. They began as a way simply to show when the
tune went up or down for the monks singing Gregorian chant. After a while,
the system developed until there were four lines, so the singer knew more exactly
which note he was meant to sing and whether it should be long 
or
short
By about 1250 it was possible to give singers more precise instructions by writing down music like this, so music could be composed for singing in parts with all kinds of complicated harmonies and the composer would know the music would sound as he or she meant it to.
