The Lord spoke to Moses, saying, "Speak to Aaron and his sons, saying, Thus you shall bless the people of Israel: you shall say to them, The Lord bless you and keep you; the Lord make his face to shine upon you and be gracious to you; the Lord lift up his countenance upon you and give you peace." (Bemidbar / Numbers 6:22-26; ESV)
Blessing is a major theme in the Scriptures. To be blessed is to be filled with the potential of life. When God created creatures - both animals and people in the book of Genesis, he said, "Be fruitful and multiply" (see Bereshit / Genesis 1:22, 28). Blessing is the opposite of cursing, which is the removal of the potential of life, such as that of the condition of a desert.
When one person blesses another, they are expressing a desire that God would fill the other with the potential of life. How blessing another person works I don't know, but it is similar to prayer in that the one doing the blessing is looking to God to honor their words and bless the one being blessed.
One of the best known blessings in the Bible is the one I quoted. God gave this particular blessing to the priests with which to bless the people of Israel. Through these words we get a better understanding as to what the blessing of God is all about. While this blessing sounds like a list, it's not. It's a poetical expression of the basic ingredients of what constitutes God's blessing.
The Lord bless you: These opening words are a general introduction to the blessing.
And keep you: "To keep" means "to watch over" like a shepherd keeps sheep. It is one thing to be filled with life, but if we are not protected by God, then the life he gives us will express itself in all sorts of ineffective ways. Many people have the Lord's blessing on their lives, but don't use it for godly purposes. Like lost sheep, their lives are on paths of destruction.
The Lord make his face to shine upon you: This is like saying, "May God smile at you." It expresses the desire that the one being blessed be in a positive relationship to him. Unless God is positively disposed toward us, then our lives will not go well.
And be gracious to you: There is nothing a human being can do to ensure they are in a positive relationship with God. It is only by a gracious act of God that anyone can be right with God. Just as Israel was chosen by God, so anyone, to be in right relationship with him, depends upon his grace.
The Lord lift up his countenance upon you: These words are a poetic parallel to "The Lord make his face to shine upon you" above. It emphasizes our need to have God's favor bestowed upon us.
And give you peace: The familiar word for peace, "shalom," means completeness or wholeness. When our lives are out of sorts, we cannot properly manage the abundant life God wants to pour out on us. It's only when we know his peace that we can experience his life.
Notice that there is no mention here of material prosperity or personal health. While the result of God's blessing may include these and other things, the essence of God's blessing is about living under the favor of God, not having stuff. It's when we know his favor - when his smile is upon us - that we are truly blessed. Then, not only are we filled with life ourselves, but that is when we become people through whom others too may be filled with life.