Groups of parties that are granted access are called qualified. In set theoretic terms they are referred to as qualified sets; in turn, the set of all such qualified sets is called the access structure of the system. Less formally it is a description of who needs to cooperate with whom in order to access the resource.
This passage describes how access to a resource is managed within a system. It uses the terms "qualified groups" and "access structure" to explain who needs to work together to get access, and how that collaboration works.