Brave New World is a novel of ideas and themes, so it isn't too concerned with plot or character.  In some ways, John is the central character of the novel, but really he isn't.  After all, he isn't introduced until half-way through the novel.

Here are some aspects to his role and character:

Foil: John is a primary foil for Bernard, the one who finds John and exploits him.  Both are idealistic and naive in their attempts to change others and the status quo.  Both are introduced by new worlds and change accordingly.

Savage: John is a "noble savage," as he is raised on the Savage Reservation.  His name comes from the verse drama The Conquest of Granada by John Dryden.  Huxley bases him on a combination of Caliban and Alonso from Shakespeare's The Tempest.  He is part slave/savage like Caliban and part civilized Utopian like Alonso.  After all, the title is taken from a The Tempest, Act V:

O wonder!  How many goodly creatures are there here! How beauteous mankind is! O brave new world! That has such people in't!

Christ-like martyr: John is a son who is split between two worlds, the natural and the supernatural.  He has two fathers, an earthly one and a mysterious other.  In the end, he dies for the sins of others: for us, the readers, and for his father, the Director.  He is meant to show us and the Director the extreme effects of both the utopia and the dystopia.  In the lighthouse, his body is in the shape similar to that of Christ on the cross.

Byronic / Tragic Hero: John takes on aspects of both, but it's hard to classify him as a classic tragic hero.  As a Byronic hero, he is "mad, bad, and dangerous to know."  He is wounded by love, exiled for his beliefs, and rebellious against authority.  As a tragic hero, he makes mistakes that lead to his death, namely participating in casual sex and taking soma.