Data visualization and analytics research has great potential to empower people to improve their lives by leveraging their own personal data. However, most Quantified-Selfers are neither visualization experts nor data scientists. Consequently, their visualizations of their data are often not ideal for conveying their insights. Aiming to design a visualization system to help non-experts explore and present their personal data, we conducted a pre-design empirical study. Through the lens of Quantified-Selfers, we examined what insights people gain specifically from their personal data and how they use visualizations to communicate their insights. Based on our analysis of 30 Quantified Self presentations, we characterized eight insight types (detail, self-reflection, trend, comparison, correlation, data summary, distribution, outlier) and mapped the visual annotations used to communicate them. We further discussed four areas for the design of personal visualization systems, including support for encouraging self-reflection, gaining valid insight, communicating insight, and using visual annotations.