Deconstruction is basically take apart certain aspects in something to bring in under a sharper focus and analyze it more closely. While comics have had their own set of rules that work for their reality, there have been times when even they take a closer look at their work and say "Hey! Does this really work after all?"
My favorite deconstruction: Batman in Tower Of Babel. It makes sense that he would have plans for in case the JL went rogue, but it was his carelessness that led to the events of that story. Also, the story didn't end with everyone forgiving him; instead they stayed mad for a good amount of time.
Worst one: Whatever the heck they were trying to do in AvX. If the whole point of it was "Don't mess with powerful things you don't understand, even if it's for the greater good", it either didn't come across or they should have targeted the Avengers instead of the X-Men. Also, things went to war too quickly even by Marvel standards. Finally, considering all of this started because Captain America got information from a very biased Wolverine, whatever they trying to say about Cyclops fell flat. In the end, both teams came off looking like morons (the Avengers moreso).