The Meaning of Moo Duk Kwan

MOO	In Korean we pronounce this "mu", and in Chinese it is "wu". It can be translated as: military, chivalry, martial. Interestingly, it is the same symbol as you see in the word WUshu, which is the generic Chinese term for martial arts. If we look at the composition of the symbol, the inner part of the symbol is the word for "stop" and the outer part means "weapon". Thus, one might argue that this character was initially intended to imply that martial arts are defensive, in that they were designed to "stop weapons".
DUK	We say "deog" in Korean. This word means: benevolence, virtue, goodness, commanding respect, etc. The character on the left means "little steps" or "to happen", and on the right the character means "moral" - hence the overall meaning of "moral steps" or "virtuous conduct" (and thus the translations I provided above). We can also break down the word for "moral" to mean "straight" (the part on the top), and "heart" (the four little lines on the bottom). Of course, moral can certainly be seen to come from "straight hearted".
KWAN	This is "gwan" in Korean, and "kan" in Japanese. It means: mansion, large building, palace or library. The breakdown of this word is quite intuitive, if you note that the symbol on the left looks like a house of sorts. And in fact, this part actually means "to eat" - which is something that (generally) happens under a roof.