"Duly noted" means to take special notice of something and mentally file it away for later reconsideration. The phrase is used both genuinely as an acknowledgment of important information and dismissively as a way to excuse a point in an argument.
"Duly" is the adverb counterpart of "due." It implies the insinuation of later consideration of a point as something that is considered when it is due. The word "duly" is often misspelled as "duelly." This may be the result of often being confused of a similar term with a different meaning, "dually noted," which literally means to take twice notice of something. The difference between the two words is extremely subtle when written or spoken, so it is important to note the context of the phrase.