孺子 is a literary term for 'child' or 'youngster', almost always encountered in classical idioms or written formal contexts. The most famous fixed expression is 孺子可教 (rú zǐ kě jiào, 'the child is worth teaching' – praise for a quick-learning young person), from the historical story of 张良 (Zhang Liang) and his mentor. Outside of idioms, modern Chinese prefers 孩子 for everyday 'child'. You would use 孺子 only when deliberately adopting a classical or elevated tone, or quoting proverbs.