"only this company can decide who can use the trademark"
It's like:
"only if it's production fulfills certain criteria can you use the name"
It's made as a consumer protection so that people can not just claim their product is this kind of "traditional" product when it isn't. Except that it's less used like a consumer protection as it's mainly used like a trademark. Controlled by a small group of people and directly profiting some regional government/economy.
Most commonly it requires the main ingredient to come from a specific region (also e.g. used for Wine or Sect).
EDIT: I kinda did throw different regulations into one explanation here.