The background to this project is the ESP8266 software we developed for general use over many months, which loosely started off as a MQTT demonstration and grew over time to become general purpose ESP8266 software written in C to make good use of the various IO pins of the ESP8266 and MQTT as a communication protocol. The peculiarities of the Nextion display is that it is normally communicated with serially. The serial lines of the ESP8266 are really needed for programming and debugging and also put out some debug info on power-up at 78k. That was really a non-starter and so a software UART was added to the code to provide a second serial line at 56Kbaud to control the Nextion.
I believe you have an errant 'r' in the title of the page :)