I understand the EPR-experiment and the Bell inequalities. I can see how dropping 'locality' solves the issue, and how dropping 'realism' solves the issue (e.g. there are really no hidden variables until you measure them)
I disagree with Danu. This is a serious question being considered by theoretical physicists involved with the foundations of quantum mechanics.
Counterfactual definiteness is an epistemological property that essentially allows you to ask what-if questions about experiments. For example, in a forensic analysis of a car crash, it might be important to know "Had the driver been going the speed limit, would the accident have happened?" or something of that nature. In essense, as per its name, a theory that possesses counterfactual definiteness allows you to use the information from an actual experiment to determine what would have happened had you changed X or Y about the setup.
Realism is a metaphysical property of a theory, which says that the objects of the theory actually exist in the world. This is in contrast to instrumentalism which says that theories are merely useful tools for predicting results, but we shouldn't take their objects too seriously. As a common example, lets take electricity: does an electron exist? A realist would say yes, and go on to define its properties and experiments that support those properties. An instrumentalist would say no, that the electron is a useful concept that we attach to a particular phenomena, but it has no independent existance. The key difference is in attitude: instrumentalists see theory as the development of ever more pragmatic tools of prediction, while realists see theory as as a series of ever more accurate representations of reality, with each "paradigm shift" (per Kuhn) providing a more nuanced picture.