This is an extremely formal and sincere apology. "誠に" (makoto ni) means "truly" or "sincerely," intensifying "申し訳ございません" (moushiwake gozaimasen), which is a humble and polite way to say "I am sorry." It's used in serious situations where deep regret or a significant mistake needs to be acknowledged.

「本当に申し訳ありません」という意味の、非常に丁寧で心からの謝罪の言葉です。