So, what exactly does synchronous multiplexing mean?
Synchronous operations are distinguished from asynchronous ones in that the former do not allow the caller to continue until they complete, whereas the latter do. Software (a)synchronicity is closely related to multithreading, and the main characteristic of select() that makes its operation synchronous instead of asynchronous is that it works entirely within a single (user) thread of execution. When you call select() your thread blocks until either one of the file descriptors you specified becomes ready, or the timeout you specified expires.
The alternative would be a programming model where you register interest in I/O on the file descriptors, then come back later to check whether they are ready.
It should be noted, however, that although select() is certainly synchronous itself, the multiplexing is mostly up to the programmer. select() provides a means to achieve it, but performs no I/O itself. It's essential brilliance is in giving you the information you need to avoid blocking trying to do I/O on one file descriptor while a different one is ready to be serviced.
Can I achieve async I/O using select?
No, select doesn't do anything to particularly facilitate asynchronous I/O. It helps you handle multiple I/O channels efficiently via a single thread, but that thread operates synchronously. This nevertheless tends to be a big win, because I/O is very slow, and that slowness is mostly associated with I/O peripherals and media, not CPU and memory. Generally speaking, a single thread has plenty of processing power to handle multiple I/O channels as long as it chooses wisely which ones to handle at any given opportunity, and select() facilitates that.
