Today (good news in part!), "meditating" is in vogue. 25 years back, you would've been considered a nut to do it. Now it's addressed as something of great health, mentally and spiritually, for a person to do. Well, OK! Great!
Scripture speaks of meditating, and, it comes not from a cultural change from five years back, but from at least about 1050 B.C.
King David of Israel at that time spoke of meditating on God’s law. We see this, for instance, in Psalm 119:97 ("Oh, how I love your law! I meditate on it all day long.”) and in Psalm 1:1-2 (Blessed is the man who does not walk in the counsel of the wicked or stand in the way of sinners or sit in the seat of mockers. But his delight is in the law of the LORD, and on his law he meditates day and night.”).
Of what David was speaking? For David, the law was a way of referring to all of Scripture . . . in his day. And in his day, Scripture consisted of the Pentateuch (the five books of Moses, Genesis - Deuteronomy), Joshua, Job, and probably Judges. Ruth was probably written during the early days of his kingship. He was writing some of the Psalms. 1 and 2 Samuel were probably not around until the days of his son, Solomon or his grandson, Rehoboam. 1 and 2 Kings recount events after his death, as do the rest of the books of the Old Testament. So, we’re looking at maybe eight books that composed the Scriptures (“the law”) during his day.
But, back on the main track, it was all of this—these eight books—that were the object of his meditation. Today, that object has grown to its final count, 66 books.
The idea of meditating on God's law means to think about it, to consider it, asking questions about it like:
~ “What import does this paragraph, story, or verse have on my life or my day today?”
~ “How does this paragraph, story, or verse correct my actions in the past (how have I been wrong and how can I get it right next time in a similar situation?)?”
~ “What does this tell me about what human beings (and I) am like and need to watch out for?”
~ and “What does this teach me about God and what He is like?”
Essentially, meditating on God’s law is thinking about the content—the teaching—of Scripture.
Hope that helps!