The sound goes through the phone system and then the receiving modem converts it back into data. The modem on the far end does the same thing, it sends sounds which get converted back to digital also. This works well as long as you have a good quiet phone system with no noise in it. After all, the noise is sound and the sound is converted into data. Bad sound means bad data.
Current modems downshift to less complex sounds to send data at a slower rate.
Inside of that box is a device called a SLC-96. It is used to save the phone company money by putting many calls on one wire and making everything digital. It sends this number mixed with everybody elses numbers, down 1 line to the phone company. Since it is digital now, it goes through their systems and arrives at the ISP, still in digital. The Slick sends sound for a telephone circuit.