"Inter" means "between" or "across." The interstate is the road between states, for instance, and international relations refers to the study of politics across the nations of the globe. "Inter-organizational" would therefore refer to things that span across multiple organizations. Examples of things that take place at an inter-organizational level include industry conferences, trade meetings, illegal monopolistic price-fixing agreements, or shared charitable ventures.
"Intra" means "within" or "inside." Intravenous medicine is giving inside the veins of the body. A company intranet is the networked connection of data and people within a company. Something "intra-organizational" would therefore apply to things within a single organization. Examples of things that take place on an intra-organizational level include competitions between different departments of a company, employee transfers from one job in a organization to another, or a program to pool sick leave and vacation days for co-workers in a disaster-stricken part of the world.