What does Psalm 34:16 mean?

Just as the Lord watches the righteous (Psalm 34:15), He also watches the wicked (Hebrews 4:13), but for a different purpose. God observes the righteous to deliver them (John 3:16–17), but He watches the wicked in preparation for judgment (John 3:36). David claims God will destroy them so thoroughly that even memories of them will be erased. In a similar statement, Solomon warned the name of those who defy God's law would "rot:" either by being forgotten or becoming repugnant (Proverbs 10:7). This verse describes God's rejection of the wicked, in contrast to the prior statement (Psalm 34:15) of God's love for the righteous.

Matthew 2 relates how, after Jesus was born, His life and those of Mary and Joseph were in jeopardy. King Herod had ordered the death of all males around Bethlehem who were two years old or under. However, God was watching. He sent an angel to Joseph to tell him to take the infant Jesus and Mary to Egypt and wait there for further word. There, we see His eyes "toward" those who love Him (Psalm 34:15). Just as God was watching over the lives of Jesus, Joseph, and Mary, He was also watching Herod, but with His face against him. Herod died while Jesus' family was in Egypt.

Acts 12 also illustrates how God watches over the righteous to deliver them but watches the wicked to destroy them. He delivered the apostle Peter but destroyed a wicked king—who happened to be the grandson of the Herod who persecuted Jesus.