Terraportation makes its first appearance in Hyperdimension Neptunia, and again in Hyperdimension Neptunia mk2. Despite the methods being different they both serve as a mode of transportation that helps travelers get from one place to another.
Hyperdimension Neptunia
In Hyperdimension Neptunia, Terraportation is a method of traveling from one landmass to another through the Sky Harbor through usage of a bridge that connects the two nations when they come into contact. However, if an individual does not signup for Terraportation with the Basilicom, then they will be unable to travel.
Hyperdimension Neptunia mk2

In Hyperdimension Neptunia mk2, Terraportation is a method of traveling by the usage of ships at the Terraportaton Terminal. It seems to be have reduced to only being used for transportation by sea rather than the main way to get from country to another as seen in the first game (Nepgear and the others had to Terraport from Lastation to Leanbox due to it being on an island away from the main landmass). In order to terraport, an individual must head to the Terraportation Terminal to board one of the ships.