In a pure discussion of definition of "links", I'd feel those offered by Ally and Tom seem most accurate from a geographical and geological point of view, and add the historical sense of it as it relates to golf.
Charles link to the Wiki list seems far too many stretch the definition and situational location, adding that if it is sand based and dunesy, well it is considered links in some sense.
For me, I prefer to just think of it as "plays firm and fast due to sand based and properly maintained turf to traditional links standards". If the sward and soil yield true bounding ground game, and interesting topography yields interesting variety and frequency of roll, tee through greens and surrounds; then who cares if the sea or water linked to town or arable farm land are a stones throw or a two day drive? It is the fun of the conditions yielded by the soil, turf, topo, and of course visits of the 4 winds to add to the joy of the game played on such in my view.
Then, when it comes to golf, it takes a well versed archie to find the course, or create the course routing, and know how to place the hazards, with due consideration to those qualities of specific turf species and soil qualities in order to design the proper construction of the hazards and features. Thus, we get the variance of the MacKenzie, prairie, or riveted style bunkers, and frequency of rolls and slope and size of greens and their surrounds. This is where I think our fun comes from, to see how various archies deal with "links or links-like" qualities in their various approaches and ideas.