A linked product is a product that is set up to display in more than one category.
This means that you only have to edit that product in one place in order to have changes take effect everywhere it is displayed. If you put it on special in one place, it will be on special in the other place/category as well.
Linking also means that you'll not see the same product appear more than once in a given list of products.
If you make a "copy" of a product, instead of linking it, then you will have two distinct and separate products which would require separate editing if you were to make changes later. Specials would affect one and not the other, unless you applied the Special to both individually. In the case of a copy, you might end up seeing both versions of the product appearing in various product lists.