This thing is commonly called a USB-to-RS232 TTL converter. It is used to directly interface a USB port on a computer to a port using a RS232 (Serial) communication protocol with a TTL (0-5V) signal.

RS-232 TTL is what the dock connector on a TI-NSpire uses. This connector can be used to bypass USB communication and interface directly with the calculator to do things that are impossible with a USB link like in this case downgrading the calculator bootcode.

Fully understanding this requires some basic knowledge in electronics, and even then trying to explain it to someone can be kinda hard. I suggest you check the Wikipedia pages on TTL and RS-232 to have a more in-depth understanding of it works. You could also look for documentation on the USB protocol, but this is way more complex, probably too much for someone with no prior knowledge of electronic communication protocols.