This paper introduces an approach that integrates self-adaptive Evolution Strategies (ES) with Large Language Models (LLMs) to enhance the explainability of complex optimization processes. By employing a self-adaptive ES equipped with a restart mechanism, we effectively navigate the challenging landscapes of benchmark functions, capturing detailed logs of the optimization journey. The logs include fitness evolution, step-size adjustments and restart events due to stagnation. An LLM is then utilized to process these logs, generating concise, user-friendly summaries that highlight key aspects such as convergence behavior, optimal fitness achievements, and encounters with local optima. Our case study on the Rastrigin function demonstrates how our approach makes the complexities of ES optimization transparent. Our findings highlight the potential of using LLMs to bridge the gap between advanced optimization algorithms and their interpretability.