to tell someone something by word of mouth: to inform them of it, or to teach it to them
At its core this word means passing something on to another person by speaking. What is passed on runs across a wide range. At one end it is simply news or a report, even a rumor: you tell someone what you have heard. At the other end it is settled teaching: you ground someone in a body of knowledge. The New Testament uses the word at both ends, so which shade is meant depends entirely on the setting.
The shared thread is that the knowledge travels by voice, from a speaker to a listener. That oral, person-to-person quality is what sets it apart from the ordinary word for teaching. It is not a technical term. Early Christians did not invent it; they borrowed an everyday Greek verb that writers of the day used for informing an official, briefing a traveler, or passing along a piece of gossip, and they stretched it toward the work of grounding people in the faith.
One caution shapes every reading of it. The English words catechism, catechize, and catechumen all descend from this verb, so it is tempting to see the formal instruction classes of the later church already fixed in the New Testament pages. They are not. The specialized church sense grew out of these early uses over the following centuries; it was not yet locked in when Luke and Paul wrote.
Nuances
Whether κατηχέω in Luke 1:4 means that Theophilus had received structured instruction in the Christian faith or only that he had been informed about it. The grammar (the preposition peri plus the matter reported) sits closer to the plain report sense used in Acts 21:24 than to the direct teaching sense of Acts 18:25, so the verse is genuinely ambiguous and the choice shapes how one pictures Theophilus and Luke's purpose. All sides now agree the later formal church catechumenate must not be read back into the verse; the question is only whether Theophilus had some structured oral instruction or merely informal report.
- majorityInstructed: Theophilus had received formal Christian teaching, so Luke writes to give him assurance about what he was already taught; the reading of most translations.; J. A. Fitzmyer, The Gospel According to Luke I-IX (AB 28), 289-301; I. H. Marshall, The Gospel of Luke (NIGTC), 43-44; D. L. Bock, Luke 1:1-9:50 (BECNT), 63-65; L. T. Johnson, The Gospel of Luke (Sacra Pagina 3)
- minorityInformed: Theophilus was an outsider learning about Christianity through preliminary reports, parallel to the report sense in Acts 21:24.; H. J. Cadbury, in The Beginnings of Christianity, ed. Foakes-Jackson and Lake; G. B. Caird, Saint Luke (Pelican); Louw-Nida, Greek-English Lexicon Based on Semantic Domains, §33.190