"And he came and dwelt in a city called Nazareth: that it might be fulfilled which was spoken by the prophets, He shall be called a Nazarene." (Matthew 2:23, KJV)
Jesus made Nazareth his permanent residence up to the age of about 30 when he officially began his ministry.
The city of Nazareth is a small town, situated in Galilee, west of Capernaum, and not far from Cana. It was built partly in a valley and partly on the slope of a hill. Populated by mostly Gentiles, the city of Nazareth is not mentioned in the Old Testament. Nazareth was considered of little significance, with a special contempt seemingly placed upon it:
"And Nathanael said unto him, Can there any good thing come out of Nazareth? . . ." (John 1:46)
The best explanation of the origin of the city name Nazareth appears to be that which traces it to the word translated Branch, (Hebrew: netzer, Strong's Concordance # H5342) in Isaiah 11:1, meaning a small twig, sprout, or sucker, which Isaiah says will come forth from the stem (or stump) of Jesse - a reference to Jesus:
"And there shall come forth a rod out of the stem of Jesse, and a Branch shall grow out of his roots: . . ." (Isaiah 11:1)
(Sources: Albert Barnes Notes on the Bible; John Gill's Exposition of the Entire Bible; Jamison, Fausset and Brown Commentary)