What does Psalm 61:1 mean?

David prays, calling upon God to hear and listen. Although the Lord was the God of Israel, the nation, He was also David's God. David called upon Him as a child needing help would call upon his father. David's prayer is offered with the assumption that the Lord will hear him and respond.

Jesus taught His disciples to address God not only reverently but also intimately. He taught them to say, "Father, hallowed be your name" (Luke 11:2). He also compared God to a father who gives good gifts to His children (Luke 11:11–13). The apostle Paul writes that God has sent the Spirit of Jesus into the hearts of believers, causing them to address God as "Abba! Father!" (Galatians 4:6). "Abba" is a familiar term, almost intimate. Only those who are born into the family of God by trusting in Jesus as Savior can say with assurance that God is their Father (John 1:12–13).