The black spot is probably the one piece of Treasure Island pirate lore that hasn't made it into broader popular culture. It's kind of what it sounds like: a circle of paper that's black on one side and has a message on the other. These are supposed to represent the will of the pirates as a group. When Pew delivers one to Billy Bones, it contains a demand for him to appear before his crewmates at a certain time. And George Merry, Tom Morgan, and Dick Johnson dare to give one to Long John Silver declaring that he is no longer their elected captain (that is, until he shows them he has the treasure map).
Jim describes Long John Silver's black spot as darkened on one side with ash, with the word "Deposed" written in ash on the reverse. But the ash has rubbed away, leaving the black spot totally unrecognizable. Perhaps this symbolizes the fleeting nature of pirate law: one minute you're in favor and the next you're out.