Spatio-temporal trajectories are crucial for data mining tasks, requiring versatile learning methods that can accurately extract movement patterns and travel purposes. While large language models (LLMs) have shown remarkable versatility through training on extensive datasets, and trajectories share similarities with natural language, standard LLMs cannot directly handle spatio-temporal features or extract trajectory-specific information. We propose TrajCogn, a model that effectively adapts LLMs for trajectory learning. TrajCogn incorporates a novel trajectory semantic embedder to process spatio-temporal features and extract movement patterns and travel purposes, along with a trajectory prompt that integrates this information into LLMs for various downstream tasks. Experiments on three real-world datasets and four representative tasks demonstrate TrajCogn's effectiveness.