The Luhn Algorithm is a formula that was developed in the late 1950s by German computer Scientist Hans Peter Luhn. It is a checksum formula used to validate identification numbers such as credit card numbers, Social Security numbers, and IMEI numbers, as well as some Canadian health insurance numbers.

The Luhn Algorithm is a fail-safe system for confirming authentication and detecting fraudulent activities involving financial accounts. It is a simple mathematical formula that helps to quickly identify and reject payments with mis-typed credit card numbers.

To compute the algorithm, common base 10 notation is used. This means that the individual digits of an account number are added together with varying weights, and are then validated against a predetermined criterion.

For instance, the algorithm requires numbers in an account to be multiplied by either 1 or 2, and then added back together. If the sum doesn't meet the predetermined criterion, then it is suggested that the card is fake. This method is often used as a quick, foolproof way to validate several digits at once.

Moreover, the Luhn Algorithm can also be used to verify a customer’s identity when they are attempting to make a purchase online. For example, when a customer attempts to purchase something, stores will inquire the customer’s credit card information, such as the credit card number, account name, and expiration date. When these details are provided, the Luhn Algorithm can use these digits to generate a checksum, which is then compared to the preset criterion. A match validates the purchase and the customer’s authenticity.

Overall, the Luhn Algorithm is an innovative and impactful mechanism used to protect financial accounts online, as well as prevent potential fraud. It enables quick and effective identification of mis-typed credit card numbers and false credentials, allowing companies to review customer transactions more efficiently and securely. Its ability to identify mistakes and fraudulent activity has made it an invaluable tool for financial institutions and applicable businesses.