Distillation is the process by which a frontier model is used to generate high-quality synthetic data to train or fine-tune a smaller LLM (an SLM).
This is important because Textbooks Are All You Need demonstrated that training an SLM with high-quality data can reproduce the quality of an LLM on specific tasks. Replacing frontier models with SLMs is advantageous because inferencing using a frontier model can be very expensive, whereas an SLM might be small enough to inference directly on a client device like your laptop.
OpenAI has a distillation API now; see Model Distillation in the API.