When tragedy strikes, it can feel as if God isn't there at all. Why would He let this awful thing happen? Why would He not deliver me from this awful situation? In truth, it is in times of trouble that God can best be found.
In context, Psalm 34 deals with the oppression of the righteous under the rule of the wicked. In fact, it is specifically a Psalm of David, when he pretended to be insane in the presence of Abimelech. Because it is a Psalm of an individual, we can apply it to the individual, unlike other "comforting" verses where a promise applied to the nation of Israel is applied to the individual.
The Psalm contrasts the wicked and the righteous. God is said to not only resist the wicked, but actually set His face against them to erase their memory from the Earth (v16). Their punishment is foretold (v21), but in the end, the profound truth of the Gospel is presented: The Lord redeems the life of His servants, and all who take refuge in Him will not be punished.
From an earthly perspective, we can understand the concept of a broken heart. Our feeble minds can barely comprehend the eternal, much less see it. As such, in times of trouble, it is only natural for us to see the trouble, and only the trouble. But it is hard to maintain such despair when we consider the joyous news that although we deserve to perish with our enemies, God Himself has provided a way out. How comforting is the message that our broken hearts are a temporary matter? A time will come when we will cease to even remember this world (Isaiah 65:17). We will forget the troubles of this life as easily as the Lord forgets the sins that caused them. Take comfort in this: God is with you. There is nothing that can happen to you that He will not set right. When your troubles make you feel as if you have been buried, in reality, the Lord may have planted you, and you will grow into a wondrous tree by His sovereign grace.