申し訳ありません (Mōshiwake arimasen) means "I am deeply sorry." This is a very formal and strong apology, conveying sincere regret and often used in serious situations or when a significant inconvenience has been caused. It's more profound than 「ごめんなさい」.

相手に深く謝罪する時に使う、非常に丁寧な表現です。ビジネスの場面などで使われます。