A cantor, more properly known as a hazzan, has no formal role in Jewish law. A hazzan is a musician trained in the vocal arts, to help lead the congregation in songful prayer.
The person leading the congregation in public prayers is the shaliach tzibbut (emissary of the congregation). Traditional Jewish law restricts hazzanim to be males over the age of 13; the non-Orthodox Jewish movements allow women over the age of 12 to be hazzans as well.
In theory, any lay person can be a shaliach tzibuur; almost every synagogue attending Jew will serve in this role at least once in their life. In practice, those with the best voice and the most knowledge of the prayesr serves much more often, and the role of cantors as a respected full-time profession has become a reality in recent centuries.
The Cantors Assembly Conservative & Masorti Judaism]
American Conference of Cantors Reform Judaism
Cantorial Council of America Orthodox Judaism