The financial services and insurance industries are currently navigating a profound structural transition, moving away from legacy, human-centric underwriting towards high-velocity, automated decision-making systems powered by machine learning and artificial intelligence. While this digital transformation has yielded unprecedented gains in operational efficiency, decision speed, and predictive accuracy, it has simultaneously introduced a "black-box" dilemma that complicates regulatory compliance and erodes consumer trust. This paper examines the critical role of Explainable Artificial Intelligence (XAI) as a bridge between the high-performance capabilities of advanced algorithms and the stringent transparency requirements of global legal frameworks, such as the General Data Protection Regulation (GDPR) in the European Union and the Equal Credit Opportunity Act (ECOA) in the United States. By analyzing the mechanics of prominent XAI methodologies - including SHapley Additive exPlanations (SHAP), Local Interpretable Model-agnostic Explanations (LIME), and counterfactual analysis—this research demonstrates how financial institutions can achieve a balance between predictive power and interpretability. Furthermore, the paper investigates the multi-layered architectural requirements for integrating explainability into underwriting workflows, ensuring that automated outcomes are fair, auditable, and free from algorithmic bias. The findings suggest that the strategic implementation of XAI is not merely a technical checkbox but a foundational component of responsible AI governance that satisfies both supervisory scrutiny and the public’s demand for accountability.