The heart is an apt symbol, but there is something more than a symbol at work here. There is the very real love of Jesus for the world, a love that wells up from both the divine as well as the human natures of Jesus. Devotion to the Sacred Heart in grounded not just in symbol, but in real love.
Here is a look at the explanation behind some of the features of the Sacred Heart:
The Cross - It symbolizes the ultimate sacrifice of love for men.
The Crown of Thorns - The suffering and agony of the Lord in His Passion and Death.
The Flames - The heart that burns with love for all of humanity.
The Wound and the Blood - His side pierced on the Cross and His blood shed for us.
Sources:
1. The Anatomy of Sacred Heart of Jesus - Catholic Link
2. Sacred Heart: A Symbol of Love and Mercy - Franciscan Media