belonging to someone else: another's, not one's own
At its heart the word marks something as belonging to someone else. Whatever it describes is not your own: another person's servant, another builder's foundation, someone else's money, even blood that is not the priest's own. The single thread running through every use is that ownership rests with another party.
From that core the meaning naturally widens. What belongs to another people or another place is "foreign," so the same word describes a strange land where God's people live as resident outsiders. And a person who is not part of your own circle is a "stranger": the sheep will not follow a voice that is not their shepherd's, and a king collects taxes from outsiders rather than from his own children. Foreignness and strangeness are not separate meanings here; they are the one idea of "not one's own" applied to lands and to people.
Its natural opposite is ἴδιος, "one's own," and the contrast between the two often carries the point of a passage.