Node Importance Estimation (NIE) is a task that quantifies the importance of node in a graph. Recent research has investigated to exploit various information from Knowledge Graphs (KGs) to estimate node importance scores. However, the semantic information in KGs could be insufficient, missing, and inaccurate, which would limit the performance of existing NIE models. To address these issues, we leverage Large Language Models (LLMs) for semantic augmentation thanks to the LLMs' extra knowledge and ability of integrating knowledge from both LLMs and KGs. To this end, we propose the LLMs Empowered Node Importance Estimation (LENIE) method to enhance the semantic information in KGs for better supporting NIE tasks. To our best knowledge, this is the first work incorporating LLMs into NIE. Specifically, LENIE employs a novel clustering-based triplet sampling strategy to extract diverse knowledge of a node sampled from the given KG. After that, LENIE adopts the node-specific adaptive prompts to integrate the sampled triplets and the original node descriptions, which are then fed into LLMs for generating richer and more precise augmented node descriptions. These augmented descriptions finally initialize node embeddings for boosting the downstream NIE model performance. Extensive experiments demonstrate LENIE's effectiveness in addressing semantic deficiencies in KGs, enabling more informative semantic augmentation and enhancing existing NIE models to achieve the state-of-the-art performance. The source code of LENIE is freely available at \url{https://github.com/XinyuLin-FZ/LENIE}.