A black box, or a mute, is a small electronic circuit added to a telephone which provided the caller with a free call. This is the opposite of a blue box where the caller has the box, in this case it's the calle. Sometimes several friends would incorporate a black box into each of their telephones to enable them to hold long conversations with each other without having to pay for them. Another use of black boxes were in the incoming modems of computers running bulletin board systems that were popular back in the 1980s and early 90s.
The way it worked
Phone phreaks figured out that by interrupting the DC current you could fool the telephone company in thinking that the phone is still on hook, and therefore not charge the caller. However this meant that they could still hear the ringing sound. But the telephone company didn't charge for phone calls that were just one or two seconds long. All you needed to do was introduce the DC current for a second to get rid of the ringing but not long enough to be charged and then you had unlimited free phone calls (or at least 15 minutes).
Building a black box
Connect a 10K ohm resistor to 'RR' and 'F' screws in an old telephone. Remove the green wire from the 'RR' screw and connect it to a toggle switch. The other end of the switch goes back to the 'RR' screw. Now identify which position of the switch gives you a dial tone and mark it as 'normal' and the other as 'free'.
When not in use keep the switch on 'normal' position. When you get a phone call pick up the phone for about 1 second and hang up, flip the switch to 'free' and pick up the phone again.