To fall ill; to become sick (intransitive). The term can sound somewhat literary or heavy compared with 'fall ill'.
年を取ると体の一部が病むことがある。
As one gets older, parts of the body may begin to ail.
彼は昨年からずっと病んでいて入院している。
He has been ill since last year and is hospitalized.
寒さで関節が病むと、動くのがつらくなる。
When joints ache in the cold, it becomes painful to move.
To suffer from (a disease); to have something wrong with (an internal organ or mental condition) — expressing suffering due to illness (transitive nuance).
彼は肺の病を長年病んでおり、治療を続けている。
He has long suffered from a lung disease and continues treatment.
心を病む人が増えているという報告がある。
There are reports that the number of people suffering from mental illness is increasing.
彼女は慢性的な痛みを病んでいて、日常生活に支障がある。
She suffers from chronic pain, which impairs her daily life.