How can a single-threaded NGINX handle so many connections?

Nginx is not a single threaded application. It does not start a thread for each connection but it starts several worker threads during start. The nginx architecture is well described in the http://www.aosabook.org/en/nginx.html.

Actually a single threaded non-blocking application is the most efficient design for a single processor hardware. When we have only one CPU and the application is completely non-blocking the application can fully utilize the CPU power. Non-blocking application means that application does not call any function that might wait for an event. All IO operation are asynchronous. That means application does not call simple read() from socket because the call might wait till data is available. Non-blocking application uses some mechanism how to notify application that data is available and it can call read() without risk that the call will wait for something. So ideal non-blocking application needs only one thread for one CPU in the system. As nginx uses non-blocking calls the processing in multiple threads has no meaning because there would be no CPU to execute additional threads.

The real data receiving from a network card to a buffer is done in the kernel when network card issue an interrupt. Then nginx gets a request in a buffer and process it. It has no meaning to start processing another request till the current request processing is done or till the current request processing requires an action that might block (for example disk read).