The main purpose of designating a "parent" is to create a hierarchy using parent/child relationships. It is used in the Galleries to create numerous levels of galleries and sub-galleries. It is also used in the Products and the Searches in a similar manner, to create numerous levels of nested items.
Here's an example galleries list showing what are the Parent galleries of different sub-galleries:
By using these parent designations, you can set up an elaborate hierarchy of galleries or searches up to 6 levels deep. Products are limited to a 3 level depth.