A foundation model is a large, general-purpose model trained on broad data and adapted (via prompting, fine-tuning, or RAG) to many downstream tasks. The term was coined by Stanford in 2021. GPT-4o, Claude, Gemini, Llama, and Mistral are foundation models for text. Stable Diffusion, Flux, and Imagen are foundation models for image.
The economics of foundation models concentrate at the largest labs because training requires hundreds of millions of dollars. Most application builders use foundation models via API rather than training their own.