Heterogeneous information networks (HIN) have gained increasing popularity for being able to capture complex relations between nodes of diverse types. Meta-structure was proposed to identify important patterns of relations on HIN, which has been proven effective for extracting rich semantic information and facilitating graph neural networks to learn expressive representations. However, hand-crafted meta-structures pose challenges for scaling up, which draws wide research attention for developing automatic meta-structure search algorithms. Previous efforts concentrate on searching for meta-structures with good empirical prediction performance, overlooking explainability. Thus, they often produce meta-structures prone to overfitting and incomprehensible to humans. To address this, we draw inspiration from the emergent reasoning abilities of large language models (LLMs). We propose a novel REasoning meta-STRUCTure search (ReStruct) framework that integrates LLM reasoning into the evolutionary procedure. ReStruct uses a grammar translator to encode meta-structures into natural language sentences, and leverages the reasoning power of LLMs to evaluate semantically feasible meta-structures. ReStruct also employs performance-oriented evolutionary operations. These two competing forces jointly optimize for semantic explainability and empirical performance of meta-structures. We also design a differential LLM explainer that can produce natural language explanations for the discovered meta-structures, and refine the explanation by reasoning through the search history. Experiments on five datasets demonstrate ReStruct achieve SOTA performance in node classification and link recommendation tasks. Additionally, a survey study involving 73 graduate students shows that the meta-structures and natural language explanations generated by ReStruct are substantially more comprehensible.