The focus is on God's relationship with the entire world. This verse describes the attributes about the God that we can "pass on" to the next generation. In verse 8 we see that God is "gracious and compassionate". The idea is that He cares about people and wants the best for our lives. He is slow to get angry at our sins and is full of love toward those who trust in Him.
 The LORD is good to all: and His tender mercies are over all His works.
This verse states that "God is good to all". There have been countless problems since Adam's sin so how can the text possibly say the LORD is good to all? To understand, this verse is describing what we might call "common grace" contrasted to "particular grace". The verse is speaking in generalities, not specifics about individual lives. God is the just judge and His judgment is certain. In the meantime we must never fail to acknowledge, It is of the LORD's mercies that we are not consumed, because His compassions fail not. They are new every morning: great is thy faithfulness. (Lamentations 3:22-23).
The word "LORD" is in all capital letters. David is using the most holy name of God to describe that He is good not just to Israelites, but to all people willing to put their trust in Him. The word "LORD" literally means, "I am what I am". Interestingly, God spends almost no space in the Bible explaining who He is, or where He came from. He just "Is who He is". This is the God we trust in and this God is full of love to all who trust in Him.