I think you're referring to the USB to UART device on the Arduino board. Older Arduinos actually had FTDI chips on them (beloved and hated by many of us in the industry)
What an FTDI chip or the Atmega16u2 (with special firmware) does is take the differential USB signal, and turn it into usable UART data that can be consumed by the main Atmega chip on the Arduino itself.
So, in other words, it's taking two completely incompatible protocols and bridging the gap so they can talk to each other. If the Arduino MCU had a USB peripheral on it, there would be no need for the USB to UART conversion (as it's done on chip!).
As for TTL, it's the architecture of how ICs were produced. Most chips these days are CMOS due to the fact that they are much lower power.
Hopefully that makes sense!