A realm was a dimension or region defined by certain properties and rules. Sometimes used metaphorically to refer to a field of study.
In 2375, Seven of Nine assumed that Species 8472 had access to a Federation database when the crew of the USS Voyager discovered a replicated Starfleet Academy and Starfleet Headquarters in San Francisco aboard Terrasphere 8 in the Delta Quadrant. Captain Kathryn Janeway later told "Boothby" to check their Federation database to learn that Janeway told the truth when she claimed that the Federation had no knowledge about the realm of Species 8472. (VOY: "In the Flesh")