What is the meaning of Luke 3:23-38?

23 And Jesus himself began to be about thirty years of age, being (as was supposed) the son of Joseph, which was the son of Heli, 24 Which was the son of Matthat, which was the son of Levi, which was the son of Melchi, which was the son of Janna, which was the son of Joseph, 25 Which was the son of Mattathias, which was the son of Amos, which was the son of Naum, which was the son of Esli, which was the son of Nagge, 26 Which was the son of Maath, which was the son of Mattathias, which was the son of Semei, which was the son of Joseph, which was the son of Juda, 27 Which was the son of Joanna, which was the son of Rhesa, which was the son of Zorobabel, which was the son of Salathiel, which was the son of Neri, 28 Which was the son of Melchi, which was the son of Addi, which was the son of Cosam, which was the son of Elmodam, which was the son of Er,

 29 Which was the son of Jose, which was the son of Eliezer, which was the son of Jorim, which was the son of Matthat, which was the son of Levi, 30 Which was the son of Simeon, which was the son of Juda, which was the son of Joseph, which was the son of Jonan, which was the son of Eliakim, 31 Which was the son of Melea, which was the son of Menan, which was the son of Mattatha, which was the son of Nathan, which was the son of David, 32 Which was the son of Jesse, which was the son of Obed, which was the son of Booz, which was the son of Salmon, which was the son of Naasson, 33 Which was the son of Aminadab, which was the son of Aram, which was the son of Esrom, which was the son of Phares, which was the son of Juda,

 34 Which was the son of Jacob, which was the son of Isaac, which was the son of Abraham, which was the son of Thara, which was the son of Nachor, 35 Which was the son of Saruch, which was the son of Ragau, which was the son of Phalec, which was the son of Heber, which was the son of Sala, 36 Which was the son of Cainan, which was the son of Arphaxad, which was the son of Sem, which was the son of Noe, which was the son of Lamech, 37 Which was the son of Mathusala, which was the son of Enoch, which was the son of Jared, which was the son of Maleleel, which was the son of Cainan, 38 Which was the son of Enos, which was the son of Seth, which was the son of Adam, which was the son of God.  (Luke 3:23-38 KJV)

Thomas Scott

Verses 23-38: Jesus is here said to have begun to be about thirty years of age at his baptism; or perhaps to have begun his public ministry, by being baptized of John when he was about thirty years old. Some understand the clause to mean, that he was  ruled, or was in subjection, to Joseph and Mary for about thirty years.—The original is certainly difficulty; the general meaning however is the same.—He was about thirty years of age when he entered on his ministry. This single decision of an inspired writer outweighs all the specious conjectures of learned men concerning the duration of our Lord’s ministry; and if he was crucified in the year A.D. 33, it must have lasted longer than they generally allow; but the word about, and the decimal number concur in warranting an opinion that he was rather above thirty at this time.—There seems no reason to doubt that the following is the genealogy of Jesus in the line of Mary: but as the names of men alone, or chiefly, stood in public registers; so the name of Joseph, not that of Mary, must have been inserted. It is therefore added, that Jesus was supposed to be the Son of Joseph; which may refer to the legal constitution, as well as to the common opinion of the Jews, as he was born of Mary after she was married to Joseph. Joseph’s father was called Jacob (Mt 1:16); but marrying the daughter of Heli, and being perhaps adopted by him, he was called his son, and as such his name seems to have been inserted in the public registers; and so the pedigree is carried backward in the line of Nathan to David, and from him to Adam, who was the son of God, as created by him in his own image, though he soon lost it by sin. Some of the same names indeed occur which are in Joseph’s genealogy; but as different persons often bear the same name, it seems needless to perplex ourselves about so common a case.—Indeed Joseph could not, in the male line, be descended both from Solomon and Nathan. Yet the arguments urged to prove that this is Joseph’s genealogy, not Mary’s, seem formed on the supposition that the female line was excluded.—Cainan (Lu 3:36) is no found in the Hebrew text in any of the genealogies, but only in the Septuagint. It is probable the evangelists transcribed the registers as sufficiently exact for their purpose, and as more generally suited to command attention, than if they had even rendered them more accurate. (Marg. Ref.)