This book is important to read because in it, Nabokov explores the limits of time and memory and seeks to transcend them. In a way, he tries to defy mortality by remembering a time before his birth and defying time's power through the creative act of re-remembering and looking at different elements of his life in different ways and forms. Note what Nabokov says about time in the following quote:
I confess I do not believe in time. I like to fold my magic carpet, after use, in such a way as to superimpose one part of the pattern upon another. Let visitors trip.
Nabokov in this text therefore tries to "trip up" his metaphorical visitors in the "magic carpet" of the form of time that he presents, as he focuses on certain parts of his life's journey from the vantage poitn of different sections of his life that subverts the normal presentation of biography as being linear and chronological. This book is important to read therefore because of the very different handling of time and life that it offers and the way that it seeks to push the boundaries of time, subverting it and seeking to control it rather than being controlled.
Of course, apart from this, the book is also fascinating in charting the life of one of the most influential literary thinkers and novelists in the 20th century and how so much of his life was spent fleeing for protection and safety. The text follows the life of the author as he first flees Russia to America and then to Switzerland. The notion of freedom is also considered in the way that Nabokov is encouraged to pursue freedom in his life through his parents. All in all, this makes a highly interesting read.