a respectful/honorific way to refer to someone else's son; 'young master' or boy (used politely).
お坊ちゃん、お父さんがお迎えに来たよ。
Young master, your father has come to pick you up.
その家の坊ちゃんはとても礼儀正しかった。
The family's son was very polite.
社長の坊ちゃんが会社を継ぐことになった。
The boss's son is going to take over the company.
a pampered young man from a well-to-do family; someone naive about the ways of the world (also the title of Natsume Sōseki's novel 'Botchan').
彼は都会で育った坊ちゃんで、苦労を知らない。
He's a city-bred young master who hasn't known hardship.
小説『坊っちゃん』は夏目漱石の代表作だ。
'Botchan' is a representative work by Natsume Sōseki.