Shealtiel was a descendent of David, and Jehozadak was in the line of Zadok the priest. These were the leaders involved in the first temple building. Haggai identifies these names in order to give a sense of legitimacy to the temple rebuilding project.1
1 In the second year of Darius the king, in the sixth month, on the first day of the month, the word of the LORD came by the hand of Haggai the prophet to Zerubbabel the son of Shealtiel, governor of Judah, and to Joshua the son of Jehozadak, the high priest: