The Bible says it plainly
John writes with unusual directness: God is love. He says it twice in a short passage, while explaining that real love begins with God rather than with our efforts to become worthy or lovable (1 John 4:8, 1 John 4:16).
This is more than saying God sometimes acts lovingly. Love is true to who he is. His love is not fickle, based on mood, or reserved for people who have already put their lives together. God takes the initiative.
He that loveth not knoweth not God; for God is love.
God showed his love in Jesus
The clearest display of God's love is not merely a feeling or a beautiful sunset. It is the sending of his Son into a broken world. John points to Jesus' death as the place where God's love dealt honestly with human sin and opened the way to life (1 John 4:9-10).
Paul makes the same point in his letter to the Christians in Rome. Christ died for people who were still sinners, not people who had earned God's welcome first (Romans 5:8). So when Christians speak of God's love, they are looking especially at Jesus, his cross, and his resurrection.
But God commendeth his love toward us, in that, while we were yet sinners, Christ died for us.
Love does not cancel God's holiness
Saying God is love does not make everything else about God disappear. Scripture also calls him holy, which means he is utterly pure and set apart from evil (Isaiah 6:3). He is just, and he does not pretend that cruelty, deceit, oppression, or sin do not matter (Psalm 89:14).
But God's holiness and justice are not rivals to his love. At the cross, God does not ignore sin, yet he gives himself in mercy to rescue people from it. That is why the Bible can speak of God as both just and the one who makes believers right with him through Jesus (Romans 3:26).
God's love changes how we live
John does not leave this teaching as an abstract idea. If God has loved us, his people are called to love one another in practical ways (1 John 4:11). That includes patience, truthfulness, forgiveness, generosity, and care for those who are easily overlooked.
No one loves perfectly. Still, God's love is not meant simply to comfort us privately. It gives us a new pattern for life. Jesus told his disciples that their love for one another would point others towards him (John 13:34-35).
If you are wondering whether God could love you personally, begin with the shape of love shown in Christ. Read 1 John 4 slowly, and notice that God's love comes before our response. You do not have to clean yourself up before turning towards him.
In this was manifested the love of God toward us, because that God sent his only begotten Son into the world, that we might live through him. Herein is love, not that we loved God, but that he loved us, and sent his Son to be the propitiation for our sins.