The concept of transitive closure can be a formidable topic to discuss, often devolving into purely mathematical discussions of binary relationships, graph theory, relationships, set theory, and so on. In plain English, transitive closure basically involves a set of origins, a set of destinations, and the paths between these origins and destinations. Given such a dataset, transitive closure provides a list of destinations that are reachable from any given origin.
You could think of this in terms of plane trips. There may not be a direct flight from Columbus, OH to Dubai in the United Arab Emirates, but if there is a flight from Columbus, OH to Toronto, Canada, a flight from Toronto, Canada to Frankfurt, Germany, and a flight from Frankfurt, Germany to Dubai, then there is transitive closure between Columbus, OH and Dubai since the trip can be made...