This research paper delves into the critical domain of network resilience within the context of the upcoming Sixth Generation (6G) communication networks. It defines 6G network resilience as the inherent ability of these advanced systems to anticipate, withstand, recover from, and adapt to diverse disruptions, ensuring continuous and high-quality service delivery for an increasingly interconnected world. The paper explores the unique demands and capabilities of 6G, highlighting its evolution from 5G and the imperative for resilience in supporting critical services and AI-native applications. It details architectural approaches such as resilience-by-design, self-healing mechanisms, the integration of non-terrestrial networks, and Zero-Trust frameworks. Key enabling technologies, including advanced Artificial Intelligence/Machine Learning, quantum networking for enhanced security and optimization, and Digital Twin (DT)-native networks for autonomous management, are thoroughly examined. Furthermore, the paper addresses significant challenges, including scalability, cost, an expanding attack surface, complex critical infrastructure interdependencies, and regulatory hurdles. Methods for measuring and evaluating 6G network resilience, focusing on quantitative metrics and service-oriented frameworks, are also discussed. Finally, the paper concludes with a forward-looking perspective on future research directions, emphasizing the necessity of embedding resilience into the very fabric of 6G networks to safeguard economic activity, public trust, and national security.