Cancelling a card or closing a credit card does hurt your credit in some cases by increasing your credit utilization ration and also lowering your average age of credit accounts.
When you cancer or close an older credit card or close a credit card that has a large credit limit, is more likely to cause a negative impact on your credit and lower your credit score.
Although if you're carrying a balance on the credit card or you need to avoid the annual fees, closing the credit card can still be a good choice for your own financial goals.
If you can you should leave the credit card open to help your credit.
Closing of the credit card removes the available credit from your total credit and it can significantly increase your credit utilization ratio which is the amount of credit that you use when compared to your total available credit.
It's recommended that you keep your credit utilization ration below 30%.
The average age of your credit accounts is also a factor in your credit score and closing an older credit card and account can reduce the average and potentially result in a lower credit score.
Also a mix of different types of credit, like credit cards and even installment loans, can impact your credit score positively and increase your credit score.
And closing a credit card and credit card account can reduce the variety of credit types which are on your credit report.