Select all objects in the target set that are adjacent to any object in the source / argument box set. Objects are adjacent if they have one or more boundary coordinates in common with no other overlaps.
Suppose we have a saved selection called Durango that selects the province of Durango in Mexico.
Running Select Adjacent selects all other provinces that share a boundary with Durango.
If Select Adjacent fails to select some "adjacent" areas but Select Touching does select those areas, carefully examine the region of adjacency to see if there is any overlap between the objects.
Select Contained / Containing