The most simple, and biblical, answer is found, by example, in the Old Testament book of Nehemiah:
They read from the book, from the Law of God, clearly, and they gave the sense, so that the people understood the reading. Neh 8:8
The ESV translators note that “clearly” = with interpretation, or paragraph by paragraph.
Adrian Warnock provides the following, based on notes from a T4G conference.
1.Expository preaching should be defined as preaching that seeks to explain the main point of the portion of the Scripture selected.
2.Expository preaching does not always have to take place as part of a long series working slowly through a book. Series can be helpful, but they need not last a decade. One-off sermons on specific verses, a chapter, or even a whole book can also be expository.
3.We must not have an overly-narrow definition of expository preaching — thinking that there is only one way to preach. Instead we must encompass the many different styles of preaching which are helpful and biblically directed. We must also understand that whilst the message of a specific verse is, of course, unified rather than divided or contradictory, its meaning is usually rich and many faceted. Because of this, different themes may be drawn out of the same passage, giving rise to very different sermons from the very same portion of the Bible.
4.Any definition of expository preaching which is too narrow and excludes the style of such men as C. H. Spurgeon, who was probably the greatest ever preacher — just has to be wrong. To criticize CHS on these grounds and fail to hold his preaching up as a model worthy of emulation today is, in my view, inexcusable. (See for example this post on Pyromaniacs.)
5.Expository preaching is not without its dangers, one of the chief of which is sounding too much like a Bible commentary read aloud.
6.Preaching needs to skillfully draw modern people into the Bible, explain the text, induce wonder, then drive the point home with a clear sense of how the people need to think, feel, believe, and act differently here in the 21st century.
7.Preaching is entirely dependent on the supernatural and sovereign activity of the Spirit, who equips both preacher and hearers for what is an impossible task and makes the words of the Bible live in its hearers hearts. Preaching needs to be passionate, emotive (though not necessarily emotional), and bring about a holy moment of experiencing the presence and voice of God through His Word.
8.Preaching God’s Word is the primary way He has ordained for people to be saved, taught, equipped, matured, and encounter God. It is the hope of the church, and a restoration of true preaching has always accompanied true revival.
9.Our preaching should be targeted at and have something relevant for each of our different audiences — the unbelieving visitor, the backslidden, the new Christian, the mature Christian, and other church leaders in the congregation. But, ultimately we are accountable to an audience of One before whom we must give an account.
10.Given the impossibility of this task, is it any wonder we need to be devoted to the study of the Word and to prayer, expressing our utter uselessness and unworthiness to proclaim God’s Word? Surely we do well to conclude that we need the help of God in our preparation, personal lives, and delivery to make us instruments that He can use. When I read about preaching I do feel that we have barely scratched the surface, and that sadly a generation exists today that has mostly never heard preaching as it should be.