Yes, you can accept them without any concern. There are numbers of ways available to accept credit cards payment online. Merchant account service is just on of the way to make it possible easily.
It is sort of account that you can set up with a bank that allows you to accept credit cards payments for online transactions. However, it's not necessary to have a merchant account to sell your products/services, but if you want to make e-shop website very professional, then a merchant account is best in your interest.
It is an account that enables merchants to accept credit card payments. It can be obtained through banks, credit card companies, or other payment processors.