The entire novel is meant to be a memorial written by John and Lorraine in memory of their friend Mr. Pignati, and so the simple answer would be that the most important character in the novel is Mr. Pignati. However, it is not the character himself but his interactions with John and Lorraine, and his ability to see people differently, that makes him important.
John's father thinks John is a "lunatic" for wanting to be an actor, and his mother spends more time cleaning the house than speaking to or spending time with him. Lorraine's mother tells her she is "not a pretty girl," and her father is no longer in the picture. The employee at the zoo says that Bobo the baboon has a "nasty disposition." Mr. Pignati, however, calls Bobo his "best friend" and treats John and Lorraine as if they were his own children, showering them with love and providing them with a place where they can feel at home—more than their parents have ever done for them.
Perhaps Mr. Pignati and Bobo are representative of each other: both are misunderstood by most but, despite this, still loved by those who have chosen to be near them and get to know them. John and Lorraine grow to love the isolated, lonely Pigman, while Mr. Pignati sees something in Bobo that no one else does, showing him love and feeding him treats.
Mr. Pignati's death also leads to certain questions and themes that are difficult to answer. Did Lorraine and John cause his death? Lorraine believes they did, although John disagrees. Did they lose a family? Does family always mean blood relatives are involved? Were they all trespassing in each others' lives, as John says? What is youth? What is old age? Mr. Pignati is the root of all these questions, but he dies at the end of the novel, leaving all the questions unanswered.