In the book The Art of Racing in the Rain, what are the turning points or significant events that affect the development of the plot?

When a reader talks about "turning points and significant events" he or she is speaking specifically about plot development.  The plot of a story is comprised of six different parts:  the exposition, the inciting incident (or conflict), the rising action, the climax, the falling action, and the resolution.  The Art of Racing in the Rain is a perfect novel to speak about these plot points as "turning points and significant events."
In the exposition, the reader learns about our narrator, Enzo, who is a dog.  Even though the crux of the story centers around Denny (the race car driver and Enzo's owner), Enzo's thoughts as narrator are very important. It is not long before Enzo begins to run into serious issues that affect the humans around him.  As Eve (Denny's wife) gets sick and begins to die of cancer, we have experienced the inciting incident or conflict of the book. Immediately, we enter the rising action as Eve's parents take Zoe (Denny's child) from Denny.  The tension rises as the trial looms.  Denny visits Zoe on weekends, and Enzo listens instinctively. Throughout all of the rising action, we learn all about Enzo's thoughts about humans.  Enzo's dreams continue when he sleeps during the trial.  Enzo dreams that he participates in the trial (with the help of a voice synthesizer) and helps everything turn out okay.  The climax (which is sometimes called the "turning point") of the story is the end of the trial when Annika recounts the events, Denny is freed, and Zoe is given back to her dad. During the falling action, we learn of Enzo's hip troubles and other issues that prove he is getting old.  It is not a surprise when Enzo dies in Denny's arms, promising to come back as a human.  The resolution of the story happens when Denny gives a very young fan an autograph.  The young fan's name is Enzo.  The reader infers, of course, that Enzo's dream of becoming "a man" has come true.