FastCGI cache in nginx works by checking if a requested resource is already stored in cache. When a client sends a request, nginx looks up the cache. If the response is cached (cache hit), nginx serves it immediately without contacting the backend server. If the response is not cached (cache miss), nginx forwards the request to the backend server, receives the response, stores it in the cache, and then serves it to the client. This process speeds up response times and reduces backend load. The configuration involves defining a cache path and zone with fastcgi_cache_path and enabling caching in the server location block with fastcgi_cache. The execution table shows the step-by-step flow from client request to cache check, backend request on miss, caching the response, and serving from cache on subsequent requests.