Hi causalset, and welcome. Thanks for the question as it gives me the opportunity to also learn something in the process. I hope the following information is helpful in your study. In the article by Wikipedia, be sure to click on their bracketed numbers which will take you into deeper explanations.
Strong's - 3480 Nazwraiov Nazoraios nad-zo-rah'-yos
from 3478; TDNT-4:874,625; n pr m
AV-of Nazareth 13, Nazarene 2; 15
Nazarite="one separated"
1) an inhabitant of Nazareth
2) a title given to Jesus in the NT
3) a name given to Christians by the Jews, # Acts 24:5 "For we have found this man a pestilent fellow, and a mover of sedition among all the Jews throughout the world, and a ringleader of the sect of the Nazarenes:"
The following link of Wikipedia seems to bring forth interesting information. Also look at its contents. http://en.wikipedia.org/wiki/Nazarene_(title)
Nazareth
The traditional view is that this word is derived from the Hebrew word for Nazareth (Nazara) that was used in ancient times.[12] "Nazareth", in turn, may be derived from either na•tsar, נָצַר, meaning "to watch,"[13] or fromne•tser, נֵ֫צֶר, meaning branch.[14]
Other suggested roots
na•tsar (נָצַר, n-ts-r), pronounced naw•tsar', meaning "to watch, guard, keep".[24] This word also has a messianic association based on a passage in Jeremiah.[25]