1The humble (kenjōgo) form of 会う ('to meet'), used when a speaker meets someone of higher status, such as a superior or business client. Common in first-meeting greetings and business settings.
初めてお目にかかります。どうぞよろしくお願いいたします。
It's a pleasure to meet you for the first time. I look forward to working with you.
来週、部長にお目にかかる予定です。
I am scheduled to meet with the department manager next week.
先日はお忙しい中お時間をいただき、お目にかかれて光栄でした。
Thank you for making time for me the other day; it was an honor to meet you.
2An archaic sense meaning 'to be visible' or 'to be recognized'; essentially unused in modern Japanese.