Tabular data provide answers to a significant portion of search queries. However, reciting an entire result table is impractical in conversational search systems. We propose to generate natural language summaries as answers to describe the complex information contained in a table. Through crowdsourcing experiments, we build a new conversation-oriented, open-domain table summarization dataset. It includes annotated table summaries, which not only answer questions but also help people explore other information in the table. We utilize this dataset to develop automatic table summarization systems as SOTA baselines. Based on the experimental results, we identify challenges and point out future research directions that this resource will support.