One interesting thing about looking at the same passage of scripture over a long time - I've been looking at this Psalm off and on for nearly three months - is that you get to look at it in order and out of order, and all kinds of different ways. I look at the parts that immediately jump out at me, but then in the process of re-reading, and re-rereading it, other sections that I initially passed over start to come into better focus. The first verse was like that, for me.
Meditation. It can be hard to know what exactly that is. What it should look like. But it's pretty clear that it plays an important role in the development of our faith and understanding of God's plans and ways. It suggests to me a continued thinking. Ongoing. Repeated. Like what you see in the story of how Joseph found himself praying in the woods in 1830:
"...my mind was called up to serious reflection and great uneasiness; but though my feelings were deep and often poignant.."
"My mind at times was greatly excited..."
"I often said to myself: What is to be done?"
"While I was laboring..."
"I reflected on it again and again..."
-Joseph Smith- History 1:6-15
In reading about meditation I came across some interesting comments from Boyd K. Packer. He took it in a direction that I'd never thought to: he talked about meditation in the context of spiritual self-reliance, and he drew a connection between that self-reliance and our ability to receive revelation.
We recognize at once that it would be folly to develop welfare production projects to totally sustain all of the members of the Church in every material need. We ought likewise to be very thoughtful before we develop a vast network of counseling programs with all of the bishops and branch presidents and everyone else, doling out counsel in an effort to totally sustain our members in every emotional need. If we are not careful, we can lose power of individual revelation. ...
Now I fear that all of [these church leaders], both in the stakes and in the University, may be doling out counsel and advice without first requiring you to call on every personal resource and every family resource before seeking a solution of your problems from the Church.
-Boyd K. Packer, Self Reliance
He talks about Oliver Cowdery's experience in trying to translate: the problem was that he wasn't trying hard enough is how I'd always thought about it, and that's true, but specifically, the Lord tells Oliver that he "took no thought" and that he should "study it out in [his] mind" -- that's meditation. And the Lord ties it directly to the ability to receive revelation (see D&C 9:7-8). Brother Packer goes on to talk about this meditative process, and emphasizes how it can't be rushed.
When you have a problem, work it out in your own mind first. Ponder on it and analyze it and meditate on it. Pray about it. I’ve come to learn that major decisions can’t be forced. You must look ahead and have vision. What was it the prophet said in the Old Testament? “Where there is no vision, the people perish” (Proverbs 29:18). Ponder on things a little each day, and don’t always be in the crisis of making major decisions on the spur of the moment.
Going back to Joseph Smith's experience with the First Vision, I'd always know that he'd put some thought into his question about which church to join, but I was absolutely stunned when I realized that it had been weighing on his mind for some two years.
This verse makes me think that meditation, like song, is a form of prayer. And that makes a certain amount of sense: the Lord knows our thoughts. He knows when we're working over a problem, and that process of pondering and meditating on something gives Him a chance to direct us, to whisper new ideas, new angles, and nudge us in the direction He knows will be best for us.