Turpentine is a Magento extension to improve Magento's compatibility with Varnish, a very fast caching reverse proxy. By default, Varnish doesn't cache requests with cookies, and Magento sends the frontend cookie with every request, causing a (near) zero hit rate for Varnish's cache. Turpentine provides Varnish configuration files (VCLs) to work with Magento and modifies Magento's behavior to significantly improve the cache hit rate.
