The Luhn algorithm generates the last digit (check-sum digit) of the credit or debit card number - the primary account number (PAN). The entire card number (PAN) should be entered to check if the number is a possible credit card or debit card. The checker cannot confirm that the credit card is valid. However, the checker will test if the sequence of numbers is not valid and therefore the card is invalid.
A check-sum digit is used frequently in other numbering systems to ensure that numbers are correctly formed and have not succumb to a transcribing error, or a basic fraud attempt.
Here is a list of other number systems that have check-sum digits calculated using the Luhn algorithm.
Read more about the Luhn algorithm HERE.