Nothing bad will happen but if you never activate the credit card after getting it in the mail then the card company will likely eventually close your account which could hurt your credit.
It also won't help build your credit if you don't use the credit card and never activate it.
Activate the credit card after getting it and then use it within reason and use only what you can pay back so you can be sure to keep the credit card account in good standing.
The longer you have the credit card account open and keep it in good standing the better your credit score will be in the future.