Medieval music is generally defined as European music written between the fall of the Roman Empire (approx 476 AD) and the middle of the 15 century. Generally speaking, the year 1400 AD is used as the benchmark for the end of the era, at which point starts the Renaissance period.
In medieval times manuscript paper was very expensive, hence the only written medieval music we have access to today comes from institutions which could afford it - basically the church and the state.
The type of music most commonly associated with the medieval ages is chanting. The chant was designed to support liturgies used when celebrating mass.
Gregorian chants are probably the best known form of chant. Basically the monks would start a second chant in parallel to the original. Typically the original tune would be sung in long notes whilst the new voice would sing many notes, often in a highly elaborate fashion.
The music of the Troubadours was usually a monophonic secular song alongside instrumentation. They would sing about war, chivalry and courtly love.
Listen to a Medieval Rock Symphony CD on the life of King Arthur - a great gift idea!