Custom Pilot is a Visual Studio Code extension framework that allows users to easily integrate custom code completion models into VS Code. It supports any API server following the OpenAI API format, specifically requiring /v1/models and /v1/completions endpoints. Users can set the API server URL in the extension's sidebar panel, choose an inference model, and enter an API key if necessary. Additionally, Custom Pilot is compatible with LM Studio, enabling users to run large language models (LLMs) locally for offline code completion.