An idiom meaning to be off-target or to respond in a way that is irrelevant or misses the point (literally, 'to face the day after tomorrow direction').
彼の答えはあさっての方向を向いていて、誰も納得しなかった。
His answer was completely off-topic and no one was convinced.
面接であさっての方向を向く受け答えばかりしてしまい、落ちてしまった。
I kept giving off-target answers in the interview and ended up failing.
その冗談は場の空気に合わず、明後日の方向を向く発言だった。
That joke didn't fit the atmosphere; it was a remark that missed the mark.