In the sermon Sinners in the Hands of an Angry God, what does Edwards mean when he says, “The bow of God’s wrath is bent, and the arrow made ready on the string?”
Throughout this sermon, one of the major points that Jonathan Edwards makes over and over again is that God is angry at all people and that all people deserve for God to be angry at them. Edwards emphasizes that God could (and perhaps should) destroy everyone and send them all to Hell, and that only his mercy prevents him from doing so. This is the meaning of the quote that you have placed in your question.
Here is the whole quote, part of which you cite:
The bow of God's wrath is bent, and the arrow made ready on the string, and Justice bends the arrow at your heart, and strains the bow, and it is nothing but the mere pleasure of God, and that of an angry God, without any promise or obligation at all, that keeps the arrow one moment from being made drunk with your blood.
When Edwards talks about “the bow of God’s wrath” he is using a metaphor. He is saying that God’s anger is very dangerous. It is like a weapon that can kill you. Then, when he says that it “is bent, and the arrow made ready on the string,” he is saying that God is ready to let his anger kill you. When an arrow is on the string of the bow and the bow is bent, the archer is ready to shoot. He has put the arrow up against the string and has pulled back. As soon as he lets go, the arrow will fly at its target. This is like having a round in the chamber of a gun with the safety off and the shooter’s finger on the trigger. In other words, this is a very dangerous situation. The person that Edwards addresses is literally a moment away from death and damnation.
By using this metaphor, and by emphasizing that God is very angry at people, Edwards meant to frighten people and also to make them grateful. He wanted them to be afraid when they realized that they deserved to be killed and damned. He also wanted them to be grateful to God for not punishing them in the way they deserved. This is what this quote means and why Edwards uses it.