Select all objects in the target set that touch any object in the source / argument box set. Objects touch if they either intersect or are adjacent to one another.
Suppose we have a saved selection called Durango that selects the province of Durango in Mexico.
Running Select Touching selects the two points and line that are entirely within Durango as well as three additional lines that are partially inside Durango. It also selects the areas that area adjacent to Durango.
Select Adjacent to
Select Contained / Containing