The phrase "Praise ye the LORD" begins these concluding chapters in this last section of the Psalter. This is one word in Hebrew, "Hallelujah". To explain it, let's begin by focusing on whom it is we are praising. Remember, when the word "LORD" is in all capitals, it is the most holy name of God. It essentially means, "I am who I am" (see Exodus 3:14). The idea is that God does not have the desire to explain where He came from or why He exists. He just exists and we must accept that fact. To expand on God's name here: "I am who I am, and we have to accept that fact in order to have a relationship with Him."
Having established the truth regarding the existence of God, we now need to praise Him. Why praise Him? The first thing to understand is that God does not need to hear our praise. It is not for His ego's sake. We praise Him in order to remind ourselves of our dependency upon Him. We praise Him in order to draw upon His power to live the life God desires us to live.
Jesus commanded us in the New Testament, And thou shalt love the Lord thy God with all thy heart, and with all thy soul, and with all thy mind, and with all thy strength: this is the first commandment. I am convinced we can't do that without drawing upon His power in order to obey those commandments in the first place.
This verse asks our "soul" to praise Him. The soul is the unseen part of us that will live forever. To understand the soul, consider the analogy of a blank DVD disk. Now imagine that same disk filled with a movie. What may surprise you is that the weight of that disk with a movie on it (without a label) is the exact same weight as it is if that same disk was blank. The real us, like that movie, has no measurable weight. When we die, the real us, called the "soul" spends eternity in heaven or hell. The point is the real us, the soul, lives forever as we have no measurable weight.
Some may ask, how does my soul praises God as opposed to my mind? When we make the effort to praise Him for the blessings in our life, the "real us" (again, the part that lives forever) is part of that praise when we do give praise to God. Our souls are praising Him when we make that effort to praise Him.
 While I live will I praise the LORD: I will sing praises unto my God while I have any being.
Verse 2 now focuses on how long one should be praising God. The idea is that we should never stop showing gratitude to Him our whole lives. We praise Him to remind ourselves that He is there guiding our lives. This has nothing to do with whether or not we have a good voice. God is not interested in our ability to sing, but in the effort on our part to praise Him. Singing to God is a privilege only for believers. Determine to praise His holy name today!