"Solipsism" is the philosophical theory that only your own mind exists, and that the physical universe and all other people are illusions. (G. K. Chesterton once questioned why a solipsist he met was trying to convince other people that his theory was true. For if it is true, there are no other people to convince.)
A "universal" is something that applies to everyone or in every place.
A "confessional" is a booth that you find in Catholic churches, where a priest sits on one side and the subject on the other, and the subject confesses his sins to the priest, using the priest as an intermediary between him and God. In a confessional a person will tell very private details about his own life, things he wouldn't normally admit to in public.
So the writer is saying that his book will not be only his own intellectual musings. He will not use the book as a confessional, that is, as a place where he can discuss private details of his own life. And he won't talk as if he himself were the entire universe, and anything that applies to him is therefore a statement about the universe as a whole.