Why do Russians say “вот он” about a wallet?

Russian has no single gender-neutral “it.” Every noun is masculine, feminine or neuter, and the pronoun follows that grammatical gender: кошелёк (wallet) is masculine, so где мой кошелёк? — вот он; тетрадь (notebook) is feminine, so вот она; a neuter noun like пальто gets вот оно. The “he” or “she” is grammar, not personality.

The ending usually tells you which: most nouns ending in a hard consonant are masculine (кошелёк → он), -а/-я is usually feminine (сумка → она), -о/-е is neuter (пальто → оно). Nouns ending in a soft sign are the trap, since they can be either: словарь is masculine, тетрадь is feminine, so learn them with their pronoun. Plural things are simply они: деньги? — они здесь.