In today's technological era, as AI systems become more integral to critical decision-making, the importance of Explainable Artificial Intelligence (XAI) has become more pronounced. It addresses the challenge of understanding complex machine learning and deep learning models, ensuring transparency, interpretability, and accountability. This research paper provides a comprehensive analysis of XAI, focusing on its significance, methodologies, challenges, and future prospects. Theoretical foundations of XAI are elucidated, clarifying key concepts such as interpretability, transparency, and accountability. We differentiate between model-agnostic and model-specific XAI methods, outlining their strengths and limitations. A range of recent XAI techniques, including Local Interpretable Model-agnostic Explanations (LIME), SHapley Additive exPlanations (SHAP), and Gradient-weighted Class Activation Mapping (Grad-CAM), are scrutinized. Through case studies in Healthcare (Pneumonia Classification), Finance (Stock Price Prediction), and Entertainment (Sentiment Analysis), we demonstrate how XAI enhances the understandability and trustworthiness of AI systems. Additionally, a comparative study of all three methods on all three case studies has been conducted, and the results are compared. Challenges such as scalability issues and ethical considerations, including biases and fairness, are discussed. Looking ahead, we offer insights into future XAI research trajectories, aiming to foster public trust and shape a future where AI systems are both intelligent and comprehensible.