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With the rapid growth and prevalence of social network applications (Apps) in recent years, understanding user engagement has become increasingly important, to provide useful insights for future App design and development. While several promising neural modeling approaches were recently pioneered for accurate user engagement prediction, their black-box designs are unfortunately limited in model explainability. In this paper, we study a novel problem of explainable user engagement prediction for social network Apps. First, we propose a flexible definition of user engagement for various business scenarios, based on future metric expectations. Next, we design an end-to-end neural framework, FATE, which incorporates three key factors that we identify to influence user engagement, namely friendships, user actions, and temporal dynamics to achieve explainable engagement predictions. FATE is based on a tensor-based graph neural network (GNN), LSTM and a mixture attention mechanism, which allows for (a) predictive explanations based on learned weights across different feature categories, (b) reduced network complexity, and (c) improved performance in both prediction accuracy and training/inference time. We conduct extensive experiments on two large-scale datasets from Snapchat, where FATE outperforms state-of-the-art approaches by ${\approx}10\%$ error and ${\approx}20\%$ runtime reduction. We also evaluate explanations from FATE, showing strong quantitative and qualitative performance.