The board in your pictures is just a breakout for connection to a PC. The USB gets connected to the miniUSB connector on the Raduino Nano. You need to add the headers and then rig up a connector for the Nano. Look up USB connections on the internet. The 3.5mm jacks are for Audio, you need to parallel them off of the audio signals from the speaker and mic. The last is to wire up a DB9 connector that some serial links use. Wiring of the DB9 would totally depend on the digital interface that you have if any.
I did not use any of the three that I got with my cases. For digital, I use the speaker and mic jacks on the front of the radio and wire the PC USB direct to the Nano for CAT control.
To sum it up, it is an option that you can use for digital mode connections, special interfaces, or not at all.