impossible dream; unattainable dream
A set phrase meaning a dream that cannot come true. The ぬ is a classical negative ending, giving a slightly literary or emphatic feel.
He kept chasing an impossible dream.
Even though I know it's an unattainable dream, I can't give up.
Standard kanji spelling using 叶う (to come true).
Kana spelling for the first part; common in informal writing.
Alternate kanji using 適う; less common and may be confused with other readings.
From 叶う (to come true) in its negative classical form 叶わぬ + 夢 (dream). The phrase is a fixed expression.