A genealogy is a list that records a person's ancestors or descendants. These lists were very important because the king would inherit his authority from his father. So the Jews used genealogies to choose the right man to become king. Most important people had records of their genealogies.
The writer uses the passive voice very purposefully in this chapter to indicate that Mary did not have a sexual relationship with anyone. She became pregnant with Jesus because the Holy Spirit performed a miracle. Many languages do not have a passive voice, so translators in those languages must find other ways to present the same truths. (See: [[rc://en/ta/man/translate/figs-activepassive]])