An internet merchant account is a bank account that merchants use to accept payments from credit cards across the internet. They are a service provided by banks. If you are running an eCommerce store and want to accept credit card payments through a payment gateway, you will need an internet merchant account.
If your business is active, you likely already have an ordinary merchant account. An internet merchant account is similar but in addition it provides extra fraud protection specific to the needs of internet transactions.
Some payment gateway companies partner with banks to provide an internet merchant account in one package with the payment gateway. In other cases, you will need to sign up for the account separately.
You can avoid needing an internet merchant account by instead using a third-party payment processor like PayPal. This makes setting up a shop easier, but there are some disadvantages to using a third-party payment processor over a payment gateway.
You can read more about internet merchant accounts at Wikipedia’s merchant account article