The New Relic OpenAI integration provides a seamless way to monitor OpenAI's GPT large language models like GPT-3 and GPT-4 at scale, helping ensure they are working as expected for important functions such as customer service and support. The integration offers real-time cost tracking and token consumption, average response time, total requests, user engagement metrics, and model performance analysis, enabling users to optimize usage, enhance ML models, reduce costs, and achieve better performance with their GPT models.