I am Hungarian, and I can completely understand the words destruction, construction, and deconstruction, although the corresponding Hungarian words are rarely used. I don't know if the con- possesses any meaning there, please explain the situation to me.
Destruction is the act of destroying something; rendering it unusable, unrepairable, broken into unusable fragments.
Deconstruction is the act of taking something apart, down to its most basic pieces. (A more common word would be disassembly.)
"Deconstruction" can also be used to refer to the theory or process behind "deconstructionism", which is "a philosophical theory of criticism (usually of literature or film) that seeks to expose deep-seated contradictions in a work by delving below its surface meaning".