1To give birth — used when a person or animal delivers offspring, or when a bird, fish, or insect lays eggs. In this literal biological sense, the standard kanji is 産む; 生む is sometimes seen but 産む feels more natural and is the preferred written form for actual birth or egg-laying.
彼女は先月、健康な女の子を産んだ。
She gave birth to a healthy baby girl last month.
うちのにわとりは毎日のように卵を産む。
Our hens lay eggs almost every day.
隣の家の犬が、先週六匹の子犬を産んだそうだ。
I heard that the dog next door had a litter of six puppies last week.
2To produce, yield, generate, or give rise to — used figuratively for bringing into existence something that wasn't there before: ideas, jobs, results, profits, misunderstandings, controversy. Common collocations include アイデアを生む (generate ideas), 雇用を生む (create jobs), 誤解を生む (give rise to misunderstanding). In this figurative sense, 生む is the standard kanji.
この政策は多くの雇用を生むと期待されている。
This policy is expected to create many jobs.
彼のチャレンジ精神が、新しい発想を生んだ。
His willingness to take on challenges gave rise to new ideas.
言葉足らずな説明は誤解を生むことがある。
An explanation that doesn't say enough can sometimes give rise to misunderstanding.
努力が必ず良い結果を生むとは限らない。
Effort doesn't always produce good results.