Asynchronous programming is a way to create programs that can execute multiple parallel tasks faster in the same process by executing code while other parts if the programs wait for I/O operations to finish, like database accesses, file accesses, network accesses, etc..
ReactPHP is a low level library similar to JavaScript Node.js that can be used to implement asynchronous programming in PHP, so you can write PHP code that can efficiently access multiple files, databases, or network computers in parallel, making everything faster.
The PHP Nuclear Reactor is library based on PIMF micro-framework that implements the MVC design pattern on top of ReactPHP.
This way you can continue to write PHP MVC components the way you are used to do, and still work well in an asynchronous programming environment based on ReactPHP.