This character is pronounced “Dang” in Korean, “Tang” in Chinese and “Too” in Japanese. It refers to the T’ang dynasty of China.
The root of the word (the “hat”, with the line that goes to the left) comes very often with signs in relation with architecture. The part inside the root is simply to suggest a certain pronunciation for the word. (In a rare composition with another Japanese character, it can be understood as “abrupt”, or “to do something in an abrupt way”.)
We say “su” in Korean, “shou” in Chinese, and “te” in Japanese. This is the word for “hand”. (Remember, for example, that karate means “empty hand”, and this is indeed the same character as you see in the Kanji text for karaTE.)
Pronounced “do” in both Korean and Japanese, and “dao” in Chinese. The simplest appropriate translation for this character is “the way”. It can also be taken to mean: road-way, street, journey, teachings, etc. Note that this is the same symbol as you would see in the expressions for karate DO, juDO, kenDO, TAOism, and others.
If we break this symbol down further, the L-shaped part is usually added to words to indicate walking or movement. The inner part of the symbol means main, and hence the translation we have used above.
Tang Soo Do can therefore be translated as : “The way of the (Chinese) empty hand”