Cell2Jack runs on a 5V USB power adapter, the same kind that charges a cell phone. You almost certainly already have a spare one, which is why the box shares power instead of adding another adapter to a drawer full of them.
Which adapter to use
Use the 5V adapter that came with your cell phone. Cheap aftermarket adapters can add a hum or buzz to your calls. If your audio has noise, the adapter is the first thing to change. See bad or noisy audio.
The 5V out port
Cell2Jack also has a 5V out port. You can run your cell phone charging cable from it to keep your cell phone charged while it sits nearby. This is optional.