What does it mean to "Bless the LORD"?

To understand what it means to "bless the Lord", lets first ask: what does it mean to bless someone. The simplest definition is "to wish someone to be well, to wish that good things would happen to that person". Here are some examples of us blessing another person: "may you be healthy !", "piece be with you !" But how can we say something like this to the almighty God ? It doesn't make any sense. What makes this question even more powerful is the fact that orthodox jews start most of their prayers with the words "Boruh ato Hashem ...", which means "Blessed are you, God ..." So jews bless God all the time - it must be important. For a long while i didn't understand what it means to bless the Lord and kind of thought that its a synonym to thank the Lord. But at one point in my life something wonderful happened to me and my heart was overflown with gratitude to God and i really wanted to express my gratitude to Him, but i couldn't find the right words. So i decided to be really honost with Him and just say whats in my heart even if it sounded childish. So what I actually said to Him was: "Dear God i thank you so much - i wish that You would be happy !" I totally realize that He is God and He is happy regardless of what i wished Him, but then i realized that by saying "I wish You happiness" i actually blessed Him. So this is as close as I personally came to realizing what it means to bless the Lord.

to Bless the L-rd simply means to Praise Him. For example, the Torah says, "When you have eaten and are full, you shall Bless the L-RD for the good land which He has given you." Deuteronomy 8.10 In Judaism this is called Birchat HaMazon Blessing or Grace After Meals. It is preceded by Psalms 126, or 137. The rabbis comment that to bless means to bend the knee. When we say "G-D is blessed," what we are really saying is that G-D is greater than and beyond all praise which we can utter and that He takes interest in the affairs of mankind by upholding the laws of the natural world in blessing us with rain and sunshine and so forth. In the above sense, G-D is truly BLESSED. "David said, Blessed are You, HaShem, the G-D of Israel our forefather from this world to the world to come. Yours, HaShem, is the greatness, the strength, the splendor, the triumph, and the glory, even everything in heaven and earth; Yours, HaShem, is the kingdom, and the soverignty over every leader." 1 Chronicles 29.10 From this, we see that to Bless the L-RD simply means to express oneself in a manner that glorifies The Holy One Blessed is He.

1. The Lord is blessed in His very being as part of His condition or state of being (along with timeless, omnipotent, omniscient, good, etc.). We can simply announce that as a way of blessing God.
2. “Blessed be the Lord” may by our desire that all know His "condition," or let all celebrate His blessed "condition."
3. Noah, Abraham, et al., blessed others with a prayer, e.g., “(May) the Lord bless you (in this way or that, by doing this or that)….” a. Could the second-fourth petitions of the Lord’s Prayer be a blessing such as typically pronounced by the patriarchs? (“hallowed by Thy name, Thy kingdom come, Thy will be done’)
4. Elizabeth’s words about Mary, “blessed are you among women,” is similar to number 1 above. Mary’s condition is that of being blessed. AB

TL; DR - essentially, it is a method of praising God and bringing him glory.

This article addresses the very issue:

There are two main things that we do when we bless the Lord. The first is synonymous with giving thanks and praise. Some translations actually say, “Give thanks to the Lord,” where others say, “Bless the Lord.” So, blessing the Lord is praising Him and giving thanks to Him—for blessing us! The other thing we do when we bless the Lord is to proclaim Him blessed. Here I think I’ll have to make a distinction between “blessed” and “blessed.” For clarity’s sake, this distinction is between “blessed” and “blest”—though I don’t really like that newfangled form of the word—the former in two syllables and the latter in one. The former is a state of being, the latter a consequence of something have been done or given to someone.

And this article also speaks about it:

Therefore, to bless the Lord means to praise Him, exalt Him and worship Him. The Psalms are filled with blessings upon God for His counsel (Psalm 16:7), His holiness (Psalm 103:1), His dominion over all things (Psalm 103:22), His honor and majesty (Psalm 104:1). We offer Him our praise and blessings because He deserves them. Unlike God’s blessings upon us, which are wholly undeserved and by His mercy and grace, our blessing God is done out of an understanding that He is the true praiseworthy Creator and our heavenly Father.

God is glorified when we bless and praise and acknowledge Him. That acknowledgement comes in the form of praise, adoration, thanksgiving and love. That is what we were originally created for. However, no man can bless God in this way unless He is right with God for we read in Proverbs 28:9: 'If anyone turns a deaf ear to the Law, even his prayers are detestable.' It is only once we have been truly blessed by God in the heavenly realms (Ephesians 1:3) that we can bless God in return, in a manner that pleases Him.