This last Sunday at church I attempted to answer this question by picking apart the passage of scripture where this phrase occurs. At the same time I figured that we might be able to answer a similar question, "What makes good preaching?" We had an issue with my microphone, so the entire message didn't record, but this topic is hugely important to me, so I'm going to make an attempt at summarizing some of that material here on this blog.
First, here is the passage of scripture:
preach the word; be ready in season and out of season; reprove, rebuke, and exhort, with complete patience and teaching.
(2 Timothy 4:2 ESV)
1) The very first thing we have to say is that good preaching is preaching THE WORD. There's that phrase, but the meaning is actually quite simple. It is not preaching opinion or preference, it is to literally preach the Word of God. This is why I believe in expository preaching. I try to pick a passage of scripture and work my way through it a verse or a few verses at a time. Topical preaching is acceptable, but even that must be done in an expository fashion. In other words, if there is a certain topic that needs to be dealt with or covered, I still need to go to the scripture to see what it has to say.
This means that I cannot preach what some preach when they preach their preferences on music styles or the ever-so-prevalent tendency to preach that the King James Authorized Version of the Bible is the only version that a person should use. If I am to preach the Word, I cannot preach these (or other) things that aren't truly based in the Word but are based on traditions, opinions, and preferences.
2) The second thing to notice here is that this preaching of the word must be done whether it is popular or not, whether it is convenient or not. Good preaching is established this way. One might say that good preaching is timeless. This doesn't mean that current cultural issues aren't addressed, but that the principles and truths from scripture are always taught.
For example, in much of America it is quite popular and well-liked to preach that one should love their enemies. This wasn't always the case, and in some places in the world it isn't the case at all. Loving your enemies would be repulsive to some cultures. Some of those same cultures would really like a preacher who focused on God's judgment or on us showing good judgment, while here in America the teachings of "judge not" are loved. Cultures change, but God's truth is timeless. Good preaching should be the same way. To preach the word rightly one must not avoid those difficult or challenging passages of scripture simply because people won't like it.
St. Augustine, Tertullian, Ignatius, Martin Luther, John Calvin, Jonathan Edwards, and Charles Spurgeon all have writings and letters and sermons that are still applicable today, not because their examples still ring true, but because they all were men who preached the Word, whether it was popular or not. Their message was timeless because the one whom they preached was timeless.
There is more to this question and more from this verse, but I will handle it in a part 2 because nobody ever reads long blog posts anyway.