Your FICO score is a snapshot number (between 300 and 850) to allow lenders to decide whether to lend you credit or not, whether to approve your loan, and the interest rate or APR that you will be offered.
Given the complexity of each person's credit history, this proprietary score makes it easy to make these thousands of credit decisions every day. This is why it's very important to know your score!
Bad scenarios: You've found the house of your dreams and you apply for a mortgage. Your income is high and you've managed to keep your debt to a minimum. You find out that your FICO is 625 and after being rejected for the mortgage, someone else snaps up the house.
Another bad scenario: Your interest rate for your car and mortgage have been several points higher than the average at the bank. Turns out there is a collections on your credit for a $5 copay from the hospital. Over the life of the mortgage and loans, you will pay tens of thousands extra.
Fortunately, you can access your credit report for free at http://www.annualcreditreport.com. This website is facilitated by the government and doesn't sign you up for any recurring credit monitoring charges that freecreditreport.com and the like do. You are allowed to request a copy of your report once a year for free from each of the three credit bureaus.
However, that will give you access to your report, but not the score that lenders use. There are now three main credit card companies that give you access to your actual FICO score for free as a benefit of the card:
Barclaycard, including the US Airways Mastercard
Citibank, including the AAdvantage cards
Of note, some companies offer "FAKO" credit scores, or scores based on their own proprietary formulas such as VantageScore, but for the most part, most lenders will rely only FICO scores.