The meaning of the phrase ‘(To) break the ice' is to restart a conversation after it has come to a deadlock. It is also used in the sense of speaking first on some delicate issue.
1. Nobody was ready to speak anything on such a delicate issue and ultimately, I had to break the ice.
2. The teacher was much irritated and there was a pin drop silence in the class; at last, our monitor broke the ice.
3. Since the long silence was getting heavy on our nerves, I decided to break the ice.