It means new "classical" music, that is to say concert music, symphonies, operas, etc., that is written by living composers.

Classical, Jazz, Adult Contemporary Pop, and Latin Music

all music. Including Techno, Rock, Jazz, Classical and basically everything else.

Yes. Almost every place has contemporary music. Today, contemporary music is usually pop music, so the contemporary Hawaiian music you hear will not sound like "Hawaiian music".

Daron Aric Hagen, is an American composer, conductor, pianist, educator, librettist, and stage director of contemporary classical music and opera.