Chazan today means a prayer-leader-cum assistant rabbi, a professional who leads services on behalf of the community. In some shuls they still wear canonicals. Chazanut is the quasi-operatic musical art of chazanim, which reached its apogee in nineteenth-century Europe. It either moves you to tears and transports you to great spiritual heights, or bores you rigid, depending on your taste.
Chazan did not always mean this. It comes from the Hebrew word meaning "to see." Chazon in the Bible is a vision. Today, chazai is the modern Hebrew for weather forecaster. In the talmudic period, a chazan mata was the guardian of a town. A chazan was also the superintendent of a school or a synagogue, where he was responsible for the smooth running of the service, assigning seats, signalling responses, etc.
The Talmud (Succah 51a) tells that the synagogue in Alexandria was so huge that the chazan would wave a flag to indicate to people when to say "Amen." From prayer supervisor it was a small step for the chazan to become the prayer leader.
A more precise term is shaliach tzibbur (shatz for short) which means agent of the community. The shaliach tzibbur is there to say the set prayers on behalf of those who are unable to recite them on their own (Shulchan Aruch, Orach Chayim, 124:1).