A blank check is a check that has already been signed but has no numerical value written in. Issuing a blank check can be very dangerous for the check owner since anyone who gets hold of the check can cash it for literally any amount. The best practice when writing checks is to always write in the amount first before signing anything.
There are situations when a blank check may be required. For example, a running bill has to be settled in several days but the account owner has to be away on that day. Since the final amount to be paid is still unknown the owner can sign a blank check and leave it with the amount to be filled in later. As was mentioned above, this can backfire so that it is only advisable if the blank check is to be left with a close and trusted person.
One way to protect oneself when writing a blank check is by indicating a limit to the amount that can be withdrawn from the account. The exact amount to be paid out is still left blank, but a notation that indicates a maximum amount that can be paid out will ensure that whoever possesses the blank check cannot get more than that amount from the bank.
The term blank check is also used metaphorically to mean having or being given a free hand or freedom to do as one may see fit.