“Neighbors” are all of the notes that are linked to the active note. Toggling neighbor links off only shows the links from the active note to its neighbors and none of the links in between the neighbors.
Here’s a simple example.
With Neighbor Links -> ‘Test Note 1’ is the active note, the other notes are neighbors, you can see the links between the neighbor notes (Test Note 5->Test Note 4, Test Note 3->Test Note 2, etc.).

Without Neighbor Links -> Now you can only see the links from the active note.

Does this help?