As Pierre said neuf is something that has not been used or has not yet had an owner, or who does not have any little traces of use, not damaged.

For example you can say:

Son ancien vélo était cassé, il a acheté un nouveau vélo. Mais celui -ci n'est pas neuf, il l'a acheté d'occasion.

=> His old bike was broken, so he bought a new one. But this one has already been used by someone, he bought it second hand.

Neuf is for something that is never used. Nouveau is for something new but not necessarly never used.