Deconstruction may refer to a couple of different things: the disassembling of some building is sometimes known as deconstruction. The popular meaning, and by far the one meant most often when the term is used, refers to a movement in the literary world. In the process of literary deconstruction, a person takes apart a story very thoroughly, to understand to the various meanings and syntax of the story. In popular culture, this practice refers only to a basic form - taking established works, usually fiction-based, and applying logic or "real life" conditions to the work and examining the results critically. Academic deconstruction is far more intensive, to the point where a companion text to a deconstructed work contains an amount of material equal to (or surpassing) the original work.
Basic deconstruction, as popularized by websites like TV Tropes, focuses on using real-world logic, thought and conditions to explain a "realistic" reaction in a work as opposed to how the work originally portrays itself. A simple example of this practice is an early comic work like Superman - the basic deconstruction of the ideas of such a comic would include the stress a hero would face as the only competent protector of an entire world, and the strain such a burden would place upon his life. As this is an elementary deconstruction, it would not explore the history and syntax used in Superman - just the general ideas.
In academic deconstruction, the French philosopher Jacques Derrida advocated the use of deconstruction as a method to arrive at a "correct" interpretation of a work. Derrida eventually concluded that an "ultimate" meaning might remain beyond human reach, but that elements of texts had no direct meaning within the texts themselves and required an outside authority for clarification. These elements included specific languages choices used in the text, references specific to a culture or many other elements.