With the purpose of attracting clicks, online news publishers and editors use diverse strategies to make their headlines catchy, with a sacrifice of accuracy. Specifically, a considerable portion of news headlines is ambiguous. Such headlines are unclear relative to the content of the story, and largely degrade the reading experience of the audience. In this paper, we focus on dealing with the information gap caused by the ambiguous news headlines. We define a new task of explaining ambiguous headlines with short informative texts, and build a benchmark dataset for evaluation. We address the task by selecting a proper sentence from the news body to resolve the ambiguity in an ambiguous headline. Both feature engineering methods and neural network methods are explored. For feature engineering, we improve a standard SVM classifier with elaborately designed features. For neural networks, we propose an ambiguity-aware neural matching model based on a previous model. Utilizing automatic and manual evaluation metrics, we demonstrate the efficacy and the complementarity of the two methods, and the ambiguity-aware neural matching model achieves the state-of-the-art performance on this challenging task.