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In the United States there are several organizations called "credit bureaus" that between them compile a credit history report for everybody in the country. These reports contain financial data, such as past loans, mortgages, credit cards and bank accounts, whether previous debts have been paid off or defaulted, and whether the person in question has ever been through the courts due to a financial matter. These agencies work with banks, courts and free information to get a solid profile, which is then sold on to the financial institutions who wish to check the credit history of a potential borrower.
Instead of trawling through stacks of financial history, it is now common for a number to be assigned in replace of a full report, making it easier for lenders to determine a borrower's creditworthiness. This is the credit score.
The big bureaus are Equifax, Experian, and TransUnion. These organizations all use the FICO software to create scores on the back of their collected financial data. Because they will all have input something different, because they'll hold differing information on a borrower, 3 scores can be passed on to a financial institution, giving them a wider scope to determine creditworthiness.
It is now not uncommon for the borrower themselves to seek out their credit score, or report in order to better grasp their own financial position. If a piece of information is incorrect or outdated it can have a serious adverse affect on getting credit. Equally if a borrower has obtained little credit over the years, they may be refused a loan on the basis that there isn't enough information to calculate their risk. It is important to build a solid credit history early on in life by making small credit card purchases.