exēgeomai

This is the plain, everyday sense of the word, and it covers five of its six appearances in the New Testament, all of them in Luke and Acts. Someone has witnessed or experienced something and now sets it out for others, point by point, the way you would give a full account of a trip or report back on a meeting.

The stress falls on telling the whole story, not just mentioning it. When Paul reports to the leaders in Jerusalem, the text says he went through what God had done item by item. The word fits formal testimony as comfortably as ordinary conversation: the same verb describes two travelers swapping news on a road and apostles giving sworn testimony before a council.

John 1:18 uses the word in a heavier sense, and it stands alone in the New Testament for doing so. After saying that no one has ever seen God, John writes that the only Son, who is closest to the Father's heart, has made him known. The word here is not simply telling a story but unveiling someone who could not otherwise be seen.

Two things mark this use as different from the everyday one. First, John leaves the word without a stated object: he does not write "made him known," he simply says "made known," and the reader supplies God from the line before. That bare construction was a recognized way of speaking in the wider Greek world, where an official expounder of sacred matters would simply expound, the subject being understood from his role. Second, the setting is the climax of John's opening hymn, which has been building toward the claim that the Son brings the unseen God into view.

This is the sense behind the modern word "exegesis": the Son is the one who sets God forth. Scholars debate how much of the old religious weight John meant to summon, but they agree on the effect. The unseen Father is disclosed not by an interpreter passing along a message from outside, but by the Son who has always been at the Father's side.