Colloquial euphemism for a man's mistress, literally 'number two'. Often used in gossip or light-hearted contexts.
彼は二号さんを囲っているらしい。
He seems to be keeping a mistress.
あの社長には二号さんがいるって噂だよ。
Rumor has it that company president has a mistress.
From 二号 (number two) + honorific さん, implying a secondary partner after the wife.