Millimeter-wave radar provides a privacy-preserving solution for human motion analysis, yet its sparse point clouds pose significant challenges for semantic understanding. We present Radar-LLM, the first framework that leverages large language models (LLMs) for human motion understanding using millimeter-wave radar as the sensing modality. Our approach introduces two key innovations: (1) a motion-guided radar tokenizer based on our Aggregate VQ-VAE architecture that incorporates deformable body templates and masked trajectory modeling to encode spatiotemporal point clouds into compact semantic tokens, and (2) a radar-aware language model that establishes cross-modal alignment between radar and text in a shared embedding space. To address data scarcity, we introduce a physics-aware synthesis pipeline that generates realistic radar-text pairs from motion-text datasets. Extensive experiments demonstrate that Radar-LLM achieves state-of-the-art performance across both synthetic and real-world benchmarks, enabling accurate translation of millimeter-wave signals to natural language descriptions. This breakthrough facilitates comprehensive motion understanding in privacy-sensitive applications like healthcare and smart homes. We will release the full implementation to support further research.