So remember that kid Liza has from an affair? That's Victor. Pnin doesn't get to meet him until he's already 14 years old. He's tall, lanky, kind of awkward, and already tired of his parents. Sounds like a regular kid to us. At least until you consider one thing.
He's pretty much a genius.
Yes, seriously. A genius. He has an IQ of 180 and is at the top of his class at St. Bartholomew's. That is one intense 14-year-old.
Just like Pnin's prerevolutionary Russian upbringing makes him out of place in basically any situation, Victor's genius separates him from everyone else. The narrator says: "To the Winds, Victor was a problem child insofar as he refused to be one. From the Wind point of view, every male child had an ardent desire to castrate his father and a nostalgic urge to re-enter his mother's body. But Victor did not reveal any behavior disorder, did not pick his nose, did not suck his thumb, was not even a nail biter" (4.3.3).
This passage tells you a decent amount about Victor and his parents. For example, it tells you that Liza and Eric need to lay off the Freud and calm down with that whole Oedipus complex thing. It also tells you that Victor is considered weird for no good reason at all. He's just non-rebellious. Shouldn't they be happy to have a well-behaved kid?
Even though Pnin and Victor only meet once, it seems clear that he's more Pnin's kid than Eric's—you know, in a metaphorical way, at least. Liza even says: "Incidentally Eric dislikes his child. He says he is the land father and you, Timofey, are the water father" (2.6.17). What that whole business about water fathers and land fathers means, we have no idea, but we do know that Eric doesn't feel like Victor's real dad.
The bowl that Victor sends to Pnin crystallizes this whole thing. The narrator reports:
'My, what a lovely thing!' cried Betty. Pnin eyed the bowl with pleased surprise as if seeing it for the first time. It was, he said, a present from Victor. [...] The bowl that emerged was one of those gifts whose first impact produces in the recipient's mind a colored image, a blazoned blur, reflecting with such emblematic force the sweet nature of the donor that the tangible attributes of the thing are dissolved, as it were, in this pure inner blaze, but suddenly and forever leap into brilliant being when praised by an outsider to whom the true glory of the object is unknown. (6.6.4)
A 14-year-old buying a crystal bowl is a little bit strange to us, but hey, the kid's a genius. And he gets his water-dad. It is probably the most beautiful thing that appears during the course of the entire novel and symbolizes a kind of deep connection between Victor and Pnin.
That's why when it appears that Pnin broke the bowl, it's such a low moment. He's already lost his job, and his future house, so if he had lost the bowl and symbolically his relationship with Victor, that would've just been the worst possible thing. At least he's got one thing going for him.