Deconstruction started out as a literary concept. Jacques Derrida, a French philosopher, described deconstruction as a style of literary analysis where "text is analyzed and broken into separate parts that work in the context of a paragraph but may contradict each other." Derrida would look at the individual parts of a commonly accepted whole and analyze how those parts interacted outside of the whole.
Jacques Derrida, looking pretty badass.
Chefs have begun serving deconstructed dishes--a traditional dish served as its component parts. Again, like a lot of things I've written about, this topic is easier to explain through example.
Take a caesar salad: lettuce, dressing (emulsion of egg yolk, anchovy, oil), crouton, parmesan cheese. A deconstructed version of this dish would present all of the flavors of a caesar salad, but with variations on temperature, texture, etc. Instead of grated parmesan, parmesan gel. A crouton becomes brioche foam. The dressing is served as a poached yolk, spherified olive oil, and a seared anchovy. The lettuce might be a sauce made from pureed romaine. The idea is that when you mix everything on the plate together, close your eyes, and take a bite, the result tastes exactly of caesar salad.
Deconstructed caesar salad from a contestant on season six of Top Chef.
Ferran Adria at el Bulli became famous for his deconstructed dishes, as did Wylie Dufresne at wd~50.
I have mixed feelings about this approach to cooking. It is definitely a novel idea and requires a great deal of creativity to execute well. However, it feels a bit superfluous, especially when an entire menu is devoted to deconstructed dishes.