I would offer a slightly different interpretation of the meaning of the term "nonlocal" than that which yulop gave (relevant information can only appear in the past light cone of some event). I agree that the issue is often expressed as an issue of whether we will relax locality or realism, but in my view, it is really only the combination of the two that we can clearly define-- when we deviate from that combination, it can be hard to pinpoint which one we relaxed!
I would say that the combination of locality and realism is the statement that the way any particle behaves is determined by information that is "carried with" the particle, so it resides both spatially and temporally with that particle at the time the particle is asked to participate in an experiment. Since the particle can only have visited its own past light cone, and any particle coming into interaction with that particle as well, that restriction includes the restriction given by yulop. (There is a detail-- virtual particles are not limited by special relativity, but their effects are, every superrelativistic influence by virtual particles has to cancel out).
Where we find a difference is if we relax the local realism, and say that the information that is required to determine an experimental outcome (or its probability) is not entirely contained in the particle involved, then we have the potential for entanglement and various other well-known quantum mechanical effects. I'm never sure why entanglement gets so much press-- there is a much more common effect that exhibits violation of local realism, and that's the Pauli exclusion principle. There is no direct interaction between particles that generates the exclusion principle-- it strictly requires a holistic treatment of a system of particles, such that the information needed cannot be carried by any of the particles themselves. Is the exclusion principle nonlocal, or nonrealistic?
I would say neither-- it is holistic. So to me, the key issue is not whether quantum mechanics violates locality or realism, because a holistic treatment is neither strictly local, nor strictly realistic, in the sense that realism here means the ability to dissect the system into independent parts that make it up. A many-particle wave function is inherently not realistic unless only the entire system is regarded as "real," and if you do that, there's no concept of locality of an entire system. So I would say that realism and locality are simply incompatible concepts in quantum mechanics, and there is no need to ask which is the one that breaks down-- it would be like asking which side of a stick breaks from the other when you snap it in half.
