That first reading doesn’t require much explanation, but it might help to put it into a broader historical setting.
In 587 b.c. the Babylonians (from modern day Iraq) led the whole citizenship of Jerusalem off as prisoners to Mesopotamia, where they employed them in constructing dikes to hold the Tigris and Euphrates fom flooding the land between them.
In 535 b.c. the Persians (modern day Iranians) conquered Babylon; and their leader, Cyrus II, declared the Israelites to have been mistreated; and he supplied them with funds to return to Jerusalem.
The Psalms tell us that the mouths of the returning Israelites were filled with laughter; but everything did not go well with them. They found they didn’t have the means or the know-how to rebuild their temple. Our reading speaks of how the prophets Haggai and Zechariah encouraged them to try.
But then, Darius, son of Cyrus II, and his son, Artaxerxces, supplied them with funds and architects to finish the temple. And, they dedicated the Second Temple it in 515 b.c..