The main reason the colonies were important to the British Empire was for money.
The colonies had a lot of land, more resources, and new animals and plants that Great Britain could use for money. Englishmen would invest their wealth into the colonies and often buy land to raise animals and crops. There were a lot of new resources in the colonies that the colonists could use and even sell overseas. New things were being found that could sell for a lot in other countries, which was making Great Britain even more wealthy.
Great Britain could also tax the colonies, which also was a way to earn money. This made the colonists angry, as they had nobody in the British Parliament to vouch for them, so they ended up boycotting a lot of British products that contained taxes on them. This eventually made Great Britain realize that taxes were not a good idea.