These three categories are categories of roles that managers must play in the course of doing their jobs.
The interpersonal role is the role that has to do with relating to other people. Managers have to act as the representative of their firm or their departments when interacting with other people. They often have to deal with other managers in other departments or in other firms. In this role, they are mainly interacting with others on a personal basis.
The informational role has to do with gathering and distributing information. Managers need to get all sorts of information about their firms. They need to get information about things like production and inventory and sales. They then need to get that information to the people both above them and below the in the firm. They may also need to give it to people outside the firm.
Finally, the decisional role is the one in which managers oversee daily operations. They must make decisions about how to resolve conflicts within their department or firm. They must decide when and if to change their procedures. They must decide how to allocate resources. All of these are part of the decisional category.