When you put something back together or rebuild it, you do a reconstruction, like the reconstruction of a neighborhood after a flood or earthquake.
Combine the prefix re-, or "again" with construction and you get a word that means "the process of putting something back together." Crime or accident reconstruction help experts figure out what really happened and possibly who is guilty or at fault, but reconstruction can also be the rebuilding of place that has been damaged, or the time of the rebuilding, like the Reconstruction era following the American Civil War.