We introduce the Brain Language Model (BrainLM), a foundation model for brain activity dynamics trained on 6,700 hours of fMRI recordings. Utilizing self-supervised masked-prediction training, BrainLM demonstrates proficiency in both fine-tuning and zero-shot inference tasks. Fine-tuning allows for the accurate prediction of clinical variables like age, anxiety, and PTSD as well as forecasting of future brain states. Critically, the model generalizes well to entirely new external cohorts not seen during training. In zero-shot inference mode, BrainLM can identify intrinsic functional networks directly from raw fMRI data without any network-based supervision during training. The model also generates interpretable latent representations that reveal relationships between brain activity patterns and cognitive states. Overall, BrainLM offers a versatile and interpretable framework for elucidating the complex spatiotemporal dynamics of human brain activity. It serves as a powerful "lens" through which massive repositories of fMRI data can be analyzed in new ways, enabling more effective interpretation and utilization at scale. The work demonstrates the potential of foundation models to advance computational neuroscience research.