AI decisions: Do we deserve an explanation? - Futurity

First, the European Union's General Data Protection Regulation (GDPR) provides that people have a right to "meaningful information" about the logic behind automated decisions using their data. This law, in an interesting and potentially radical way, seems to mandate that any automated decision-making that people are subject to should be explainable to the person affected. That got me wondering: What does that mean? How do we implement that? And what does explanation really mean here?