to come down: to travel or move from a higher place, region, or point down to a lower one
The word joins "down" to the ordinary verb "to come," so at its root it means to come or go down. In the New Testament it is almost entirely travel vocabulary. Luke reaches for it again and again in Acts to move people from one place to another, and it appears almost nowhere else.
Much of the "down" is plain geography. Jerusalem and the hill country of Judea stand high, so leaving them is spoken of as going down, whether the traveler is heading for the coast, for Antioch, or for Caesarea. The same word carries Jesus down from Nazareth to lakeside Capernaum and the disciples down from the mountain where he was transfigured.
At sea the verb becomes a settled term for reaching shore: a ship "comes down" to a port, which English renders "landed" or "put in." Once, in the letter of James, the motion is heavenly rather than earthly, describing what a certain kind of wisdom does or does not do in coming from above.
Greek has a far more common everyday word for going down, καταβαίνω, used for stairs, rain, and descents of every kind. This verb is the more literary choice Luke favors when he narrates a journey.