Large Language Models (LLMs) have revolutionized various fields with their exceptional capabilities in understanding, processing, and generating human-like text. This paper investigates the potential of LLMs in advancing Network Intrusion Detection Systems (NIDS), analyzing current challenges, methodologies, and future opportunities. It begins by establishing a foundational understanding of NIDS and LLMs, exploring the enabling technologies that bridge the gap between intelligent and cognitive systems in AI-driven NIDS. While Intelligent NIDS leverage machine learning and deep learning to detect threats based on learned patterns, they often lack contextual awareness and explainability. In contrast, Cognitive NIDS integrate LLMs to process both structured and unstructured security data, enabling deeper contextual reasoning, explainable decision-making, and automated response for intrusion behaviors. Practical implementations are then detailed, highlighting LLMs as processors, detectors, and explainers within a comprehensive AI-driven NIDS pipeline. Furthermore, the concept of an LLM-centered Controller is proposed, emphasizing its potential to coordinate intrusion detection workflows, optimizing tool collaboration and system performance. Finally, this paper identifies critical challenges and opportunities, aiming to foster innovation in developing reliable, adaptive, and explainable NIDS. By presenting the transformative potential of LLMs, this paper seeks to inspire advancement in next-generation network security systems.