Then you've already failed. Getting a layman's explanation of a topic should not require one to become the equivalent of an undergrad in that topic.
What you should be saying is "Deconstruction is an approach, introduced by French philosopher Jacques Derrida, which rigorously pursues the meaning of a text to the point of exposing the contradictions and internal oppositions upon which it is apparently founded and showing that those foundations are irreducibly complex, unstable or impossible" (courtesy wikipedia).
And then the layman asks "how does this approach expose contradictions?"
And you say "Deconstructions work entirely within the studied text to expose and undermine the frame of reference, assumptions, and ideological underpinnings of the text. Although deconstructions can be developed using different methods and techniques, the process typically involves demonstrating the multiple possible readings of a text and their resulting internal conflicts, and undermining binary oppositions (e.g. masculine/feminine, old/new)."
and there we have it, good enough for the layman to realize it's a line of thinking he's probably not interested in pursuing anymore. And then...if they keep on that, you say, "this is getting a bit into the deep end for me to make it simple and explainable, if you are really interested, start by reading these books first."
What you should be saying is "Deconstruction is an approach, introduced by French philosopher Jacques Derrida, which rigorously pursues the meaning of a text to the point of exposing the contradictions and internal oppositions upon which it is apparently founded and showing that those foundations are irreducibly complex, unstable or impossible" (courtesy wikipedia).
And then the layman asks "how does this approach expose contradictions?"
And you say "Deconstructions work entirely within the studied text to expose and undermine the frame of reference, assumptions, and ideological underpinnings of the text. Although deconstructions can be developed using different methods and techniques, the process typically involves demonstrating the multiple possible readings of a text and their resulting internal conflicts, and undermining binary oppositions (e.g. masculine/feminine, old/new)."
and there we have it, good enough for the layman to realize it's a line of thinking he's probably not interested in pursuing anymore. And then...if they keep on that, you say, "this is getting a bit into the deep end for me to make it simple and explainable, if you are really interested, start by reading these books first."