A counter check is a check with blank spaces for the account information. Banks give these out to customers who have not yet received pre-printed checks. They may also give them to customers who have no other means of withdrawing cash from their accounts.
Since counter checks rely on handwritten account information, many businesses don't accept these as a form of payment due to the potential for fraud. Some banks have the capability of printing a small number of starter checks with official account information. This allows new account holders to immediately gain the ability to access the funds in an account.