The title refers to the French Revolution and the problems with the Manette family.
Charles is arrested because of his family’s crimes, and because of this Sydney Carton, Jarvis Lorry, Dr. Manette, Lucie, and their daughter go to France to try to rescue him. The storm was foreshadowed. In Book II, Chapter 21, there was a warning.
But, there were other echoes, from a distance, that rumbled menacingly in the corner all through this space of time. And it was now, about little Lucie’s sixth birthday, that they began to have an awful sound, as of a great storm in France with a dreadful sea rising. (21)
Dickens likes to use the metaphor of the storm to describe the revolution because it gathers slowly and then gets more and more forceful, and then becomes violent and destructive. At first, the revolution was just a whisper, kind of like wind is when a storm is first getting started. Then, as the revolution got more and more dangerous, it got louder and louder as the revolutionaries began to act and got bolder.
The storm did not affect the Manettes right away, except at Darnay’s trial. Then Lucie fell in love with Darnay, and Dr. Manette had to make a choice. He decided that he would not say anything, and he would let his daughter be in love with the man whose family had imprisoned him.
In France, the Manette family faces utter destruction. They are facing their own personal storm as well as the storm of the revolution. Sydney Carton makes a choice of his own. He decides that he must sacrifice his life for Lucie. In a way, the storm for him is internal. He will lay down his life for the woman he loves. He knows he cannot have her, so he will make sure that she can be happy, even if it means that he is no longer with her. He is helping her in the only way he can.
To him, his miserable life is not worth anything. Her life is all that matters. Still, it cannot be easy for him. He changes places with Darnay, taking advantage of their remarkable resemblance. Darnay would not do this willingly because he is too noble. Carton knows this. He plans everything to the detail and succeeds. In the end, the Manettes survive and the revolution rages on without them.