This is from a blog post on the Gospel Coalition website.
1. It is the method least likely to stray from Scripture.
If you are preaching on what the Bible says about self-esteem, for example, undoubtedly you can find some useful insights. But even when you say entirely true things, you will likely abstract them from the Bible's central story line. Expository preaching keeps you to the main thing.
2. It teaches people how to read their Bibles.
Especially if you're preaching a long passage, expository preaching teaches people how to think through a passage, how to understand and apply God's Word to their lives.
3. It gives confidence to the preacher and authorizes the sermon.
If you are faithful to the text, you are certain your message is God's message. Regardless of what is going on in the church—whether it is growing or whether people like you—you know you are proclaiming God's truth. That is wonderfully freeing.
4. It meets the need for relevance without letting the clamor for relevance dictate the message.
All true preaching is properly applied. That is of extraordinary importance in our generation. But expository preaching keeps the eternal central to the discussion.
5. It forces the preacher to handle the tough questions.
You start working through text after text, and soon you hit passages on divorce, on homosexuality, on women in ministry, and you have to deal with the text.
6. It enables the preacher to expound systematically the whole counsel of God.
In the last 15 years of his life, John Calvin expounded Genesis, Deuteronomy, Judges, Job, some psalms, 1 and 2 Samuel, 1 Kings, the major and minor prophets, the Gospels in a harmony, Acts, 1 and 2 Corinthians, Galatians, Ephesians, 1 and 2 Thessalonians, and the pastoral epistles.
I'm not suggesting we organize ourselves exactly the same way. But if we are to preach the whole counsel of God, we must teach the whole Bible. Other sermonic structures have their merits, but none offers our congregations more, week after week, than careful, faithful exposition of the Word of God.