Banks use your credit score to decide the terms of loans extended to you: that is, how much money they'll give you and what the interest rate and terms will be. The better your credit score, the better your loan terms. Lower interest rates, especially on something substantial like a home mortgage, can save you many thousands of dollars over the life of the loan, so a good credit score is worth striving for.
Getting Free Scores
There are an infinite number of ways your credit score might be calculated. Credit scores from different sources may be plotted on different scales (e.g., FICO Score: 350-850; PLUS Score: 330-830) and may be designed to measure very different things, yielding scores that may differ by a large number of points. Credit Sesame provides Experian’s National Equivalency Score (360-840), while Credit Karma uses the TransUnion TransRisk and VantageScore (300-850) models. The FICO score is the model most often used by banks, but it is never available for free; the VantageScore is the second most common. Other, more simplistic models, like Experian's PLUS score, are only meant to be used for 'educational purposes' and are not used by lenders. If your bank offers a free score, look up the scoring model they use. Though these values are useful primarily in a relative context, it is still valuable to know how you score comparatively.