to exchange one thing for another: to swap, substitute, or change something out
At its core the word describes a trade: someone hands over one thing and takes another in its place. The law of the dedicated tithe uses it plainly, warning that a worshiper may not exchange an animal already promised to God, a good one for a bad or a bad for a good (Leviticus 27:10). Once something belongs to God, no cheaper stand-in may be quietly substituted for it.
The prophets take this everyday word and turn it into a picture of betrayal. Exchanging is harmless when the trade is fair; it becomes tragedy when a people trade away the one thing worth keeping. Israel "exchanged their glory," their God, for the image of a grass-eating ox (Psalm 106:20), and Jeremiah is stunned that even pagan nations do not swap out their gods, worthless as those are, while Israel traded the living God for what cannot help (Jeremiah 2:11). The Greek New Testament sounds the same charge, that people exchanged (ἀλλάσσω) the glory of God for an image (Romans 1:23).
A third shade drops the second object and simply means to change or alter. A person of integrity swears to his own hurt and does not change his word (Psalm 15:4); Moab, never poured from vessel to vessel, keeps its taste and its scent is not changed (Jeremiah 48:11); the faithful refuse to fear even though the earth itself gives way and changes. The one thread through every use is that something is no longer what it was, most often because it was traded for something else.