the arrival of a person and the presence that follows: someone's coming and being there
At its root the word names two sides of one event: a person arriving, and that person now being present. The opposite of this word is absence, and Paul sets the two side by side when he speaks of his being there with the Philippians as against his being away from them. So whether the focus falls on the moment of arrival or on the staying that follows, it is the same idea: a particular person has come and is now here.
In the wider Greek world the word had picked up a special use for the official visit of a king, an emperor, or a governor to a city, an arrival staged with great ceremony, and a parallel use for a god showing up in power to help. The New Testament writers do not lock the word into that grand sense. Paul uses it just as readily for the arrival of traveling friends, for his own unimpressive showing in person, and even, with bitter irony, for the counterfeit arrival of the man of lawlessness who works by Satan's power.
The word becomes weighty only when it is attached to the Lord. By far its most frequent use is for the Coming of Christ, his future arrival in glory as king and judge. That force does not live inside the word itself; it comes from naming Christ as the one who arrives. The ceremonial background of a royal visit gives the picture its color: the King is coming, and his people go out to meet him.