A blank check often refers to a check that has been signed by an authorized check signer before the other information (date, payee, amount) has been entered on the check. For instance, a small business owner may sign three blank checks before leaving for a seven day vacation. Basically the owner is trusting that the employee holding these checks will enter the information required to make up to three business payments in the owner's absence. This is obviously poor internal control since the employee is able to issue the check for any amount and to any person. In addition these blank checks must be stored in a very secure place since anyone else could also complete the check information.
A blank check could also refer to the completely blank checks that are received from a check printing company. These blank checks do not yet have an authorized signature and are sometimes referred to as check stock. These checks should be stored in a secure place until they are inserted into the company's printer in order to pay its suppliers, etc.
Lastly, blank check sometimes indicates that a large, uncertain amount has been authorized in order to accomplish something. For example, a rich grandparent might indicate that an only grandchild will have a blank check as far as the cost of education.