The code uses V-USB to create a USB keyboard. V-USB is a software package that allows you to make USB devices out of AVR microcontrollers.
Instead of explaining using text, I have a video tutorial about how to build a USB keyboard:http://www.frank-zhao.com/index.php?page=usnoobie_rfid_keyboard
Please note that this two part video is over 15 minutes in total. I've put an incredible amount of effort into the video. Please watch it in 720p full screen so you can read all the text.
I also have another Instructable that will explain more USB and V-USB stuff to you: https://www.instructables.com/id/USB-Wii-Classic-Controller/
The differences between the RFID USB Keyboard and this USB PCB Business Card is that the ATtiny85 is used instead, and the text comes from internal flash memory instead of a serial port. One important aspect to note is the fact that the ATtiny85 uses an internal PLL to generate the clock speed that V-USB requires.
Also read my other USB instructable involving creating more USB devices, where I explain the USB bus, descriptors, and other aspects in more detail.