The easiest way to explain the mad lib is that it is an oversimplification of Derrida's ideas on signifier/signified, that way its understood that it isn't an exact representation but more of a possible example. Derrida has this idea that signifier and signified are, as Sauccer states, arbitrary but on top of that because language is in a constant shift, no actual meaning can be forced on any words. Also because language is shifting, many words have multiple context or meanings and that through translating or even speaking, these loose meaning therefore you're not able to fully explain the meaning of anything, you can only attempt to persuade, kinda like rhetoric's. These fluctuations make it so binary opposition can exist. The mad lib is an example of arbitrary word shifts and a possible way of explaining language shift in an accelerated fashion. Examples of how it specifically relates: in the introduction of Derrida there is mention made about trace. The way this works is that the signifier can illicit any numbers of signified that might not normally match it. This stems from 'trace' connections in past derivations of language which allow for the shifting of meaning to occur. This moves into DifferEnce vs DifferAnce. Originally the pronunciation was the same and the only way to discern the meaning was through writing. So verbal and even contextually it wasn't always obvious, hence meaning is fluid. Language changed and differAnce was pronounced differently to allow for distinction to occur.
Derrida (French speaking parents/Jewish decent) work on this idea of Deconstruction started post World War II (1949) in France. And after that came the Algerian war (54-62) for independence from France, where french nationalism was in constant flux. His initial frame work for what he would later continue was published in the 1960's. Dissemination was published in 1972 after some time in Harvard.
He thought structuralism was limited but had good basic principles that he decided to go beyond. He wants to break everything down to the basic principles, essentially destroying the privileged binary (hierarchy and creating a balanced continuum) He doesn't want to exclude meaning but to allow for multiple aspects to emerge. It's a type of new enlightenment. Believes that old 'truth' isn't working so break things down in order to build it back up the right way
It also is new way of criticizing literature and political institutions The rise of deconstruction happens after WWII and in Derridas personal life the Algerian war, so its criticizing the the literature, philosophy and social/political structure that allowed this these instabilities to happen. Writing, philosophy and government were flawed are what actually allowed wwii happen so this response to this
To make people see a new way of thinking. That more possibilities exist. To destroy narrow mindedness of and/or through binary opposition possibilities. Everything we do is about translation. It really is a way of being able to restructure things that have so far failed to work previously. It also allows literature to transcend meanings that have preceded in the past. In the aspect of the political realm it allows for change to occur without any 'textual' change.