People generally credit methodology changes under the term 'community policing' for the turn-around. Basically, the idea is that rather than just riding in, cracking skulls, slapping cuffs on once a night, engage with the community more, address more stuff like noise complaints and vandalism, to build relations with the community and coincidentally crack down on the same troublemakers a lot of the time. In theory (and in practice), it turns out to be more effective at stopping crime from happening than the deterrent factor of riding in lights blazing every night.
(This isn't to say that NYC cops are perfect or that stop-and-frisk doesn't happen all the damn time, just outlining the general theory behind community policing)