  As AI is more and more pervasive in everyday life, humans have an increasing
demand to understand its behavior and decisions. Most research on explainable
AI builds on the premise that there is one ideal explanation to be found. In
fact, however, everyday explanations are co-constructed in a dialogue between
the person explaining (the explainer) and the specific person being explained
to (the explainee). In this paper, we introduce a first corpus of dialogical
explanations to enable NLP research on how humans explain as well as on how AI
can learn to imitate this process. The corpus consists of 65 transcribed
English dialogues from the Wired video series \emph{5 Levels}, explaining 13
topics to five explainees of different proficiency. All 1550 dialogue turns
have been manually labeled by five independent professionals for the topic
discussed as well as for the dialogue act and the explanation move performed.
We analyze linguistic patterns of explainers and explainees, and we explore
differences across proficiency levels. BERT-based baseline results indicate
that sequence information helps predicting topics, acts, and moves effectively
