The task of detecting morphed face images has become highly relevant in recent years to ensure the security of automatic verification systems based on facial images, e.g. automated border control gates. Detection methods based on Deep Neural Networks (DNN) have been shown to be very suitable to this end. However, they do not provide transparency in the decision making and it is not clear how they distinguish between genuine and morphed face images. This is particularly relevant for systems intended to assist a human operator, who should be able to understand the reasoning. In this paper, we tackle this problem and present Focused Layer-wise Relevance Propagation (FLRP). This framework explains to a human inspector on a precise pixel level, which image regions are used by a Deep Neural Network to distinguish between a genuine and a morphed face image. Additionally, we propose another framework to objectively analyze the quality of our method and compare FLRP to other DNN interpretability methods. This evaluation framework is based on removing detected artifacts and analyzing the influence of these changes on the decision of the DNN. Especially, if the DNN is uncertain in its decision or even incorrect, FLRP performs much better in highlighting visible artifacts compared to other methods.