After being admonished by a parent, teacher, or boss, Koreans often respond to the admonishment by saying, 알겠습니다, which always seemed a little strange to me. Why would Koreans use the future tense (겠) with 알다 (to know)?
Well, today I looked up 알다 and found that it has many meanings, including the meaning of "to remember." Therefore, I am guessing that 알겠습니다 means, "I will remember" (what you said). Instead of 알겠습니다, you can also say, "명심하겠습니다," which means, "I will take (your words) to heart."
Mr. Lee Su-yeol (이수열) does not like 알겠습니다, but I do not see any problem with it, at least, not after learning that 알다 can mean "to remember."