her words like a picture puzzle, and as I did, so my own life was rebuilt."

This work is the author's autobiography. The chapters are narrated in the first person by the author's mother and by the author himself. He describes his struggle to find his identity through exploring his mother's story. In the quote above, he likens his search to a child, constructing his life out of Tinkertoys. His mother's words are like the Tinkertoys. He uses her memories like a puzzle, to put together the story of his life. He was able to "reconstruct" his life from her words.

Tinkertoys were wooden toys that one fit together to make all sorts of things - the precursor to Leggos, only Tinkertoys had round wooden wheels with holes in them and long spindles that fit into each other.  You are no doubt too young to remember them but if you want to see what the looked like, do an online search.