What was a Committee of Correspondence? It was just people, like you and me, who had something in common and they wanted to talk about it. It was difficult to travel in colonial times, so instead, they wrote each other letters. These letters were passed from person to person, with people adding comments and responses. It wasn't the quickest way, but it worked.
Committees of Correspondence sprang up in the Massachusetts colony. These committees wrote each other about colonial matters.
Pretty soon, similar committees were formed in other colonies. These groups began corresponding with each other.
Each time these committees criticized British policies, they were breaking British law. In the 1700s, under British law, it was illegal to criticize the British government, even if the criticisms were true. This same law applied in the colonies until 1735. After that time, the colonists developed a tradition of freely criticizing the government.
The British officials in the colonies knew how angry colonial leaders were about taxation without representation. To avoid additional conflict, they did not try to enforce that particular British law. Nor did they try to stop committees from gathering or communicating.
By doing so, the British gave the colonists an opportunity to discuss issues and formulate a plan of action should one be needed. And it gave colonial leaders a sense of unity and reinforced their belief in their right to free speech and the right to gather.