Those are curse tablets, called defixiones. You can find a pretty extensive catalog of them here. Basically, they were a form of physical magic in which a particular spell would be written on the it (eg, "I call upon the gods of x and y to rend limb from limb person z who stole my money"), the tablet would be pierced to "fix" the incantation onto the physical object, then it would be buried in a significant spot. Details varied enormously--it is pretty common, for example, to find no writing at all, or no piercing, or find it written on wood or papyrus. The spells vary from agricultural protection against pests to love spells to curses on a disliked chariot team.

The procedure in Rome is reasonably accurate and I believe the incantation is adapted from a real tablet, but often the actual curse making would be done by a professional magician who would be commissioned to cast a particular spell.

There is a great deal of work done on this and it is one of the most fascinating classes of archaeological remains we have. I would be happy to try to answer any specific questions.