Understanding human mobility patterns is essential for various applications, from urban planning to public safety. The individual trajectory such as mobile phone location data, while rich in spatio-temporal information, often lacks semantic detail, limiting its utility for in-depth mobility analysis. Existing methods can infer basic routine activity sequences from this data, lacking depth in understanding complex human behaviors and users' characteristics. Additionally, they struggle with the dependency on hard-to-obtain auxiliary datasets like travel surveys. To address these limitations, this paper defines trajectory semantic inference through three key dimensions: user occupation category, activity sequence, and trajectory description, and proposes the Trajectory Semantic Inference with Large Language Models (TSI-LLM) framework to leverage LLMs infer trajectory semantics comprehensively and deeply. We adopt spatio-temporal attributes enhanced data formatting (STFormat) and design a context-inclusive prompt, enabling LLMs to more effectively interpret and infer the semantics of trajectory data. Experimental validation on real-world trajectory datasets demonstrates the efficacy of TSI-LLM in deciphering complex human mobility patterns. This study explores the potential of LLMs in enhancing the semantic analysis of trajectory data, paving the way for more sophisticated and accessible human mobility research.