In recent decades, the weather around the world has become more irregular and extreme, often causing large-scale extended power outages. Resilience - the capability of withstanding, adapting to, and recovering from a large-scale disruption - has become a top priority for the power sector. However, the understanding of power grid resilience still stays on the conceptual level mostly or focuses on particular components, yielding no actionable results or revealing few insights on the system level. This study provides a quantitatively measurable definition of power grid resilience, using a statistical model inspired by patterns observed from data and domain knowledge. We analyze a large-scale quarter-hourly historical electricity customer outage data and the corresponding weather records, and draw connections between the model and industry resilience practice. We showcase the resilience analysis using three major service territories on the east coast of the United States. Our analysis suggests that cumulative weather effects play a key role in causing immediate, sustained outages, and these outages can propagate and cause secondary outages in neighboring areas. The proposed model also provides some interesting insights into grid resilience enhancement planning. For example, our simulation results indicate that enhancing the power infrastructure in a small number of critical locations can reduce nearly half of the number of customer power outages in Massachusetts. In addition, we have shown that our model achieves promising accuracy in predicting the progress of customer power outages throughout extreme weather events, which can be very valuable for system operators and federal agencies to prepare disaster response.