When you carry more than one credit card, it can affect your credit score in many ways. It can be a positive thing or a negative thing.
It can be negative when the only type of credit you have is in the form of credit cards. Your credit should be diversified among various forms of credit and not just credit cards. It could also hurt your credit score if your cards are all new. Your credit score could also suffer if your balance on each card is high.
The primary way having multiple cards can help your score is if you make all your payments on time, every time.