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The Yield Curve (YC) is just the graphic representation of what investors think will happen to interest rates in the future. The most common YC that gets put in books and in the news is the yield curve of U.S. Treasury securities. This YC can impact the YC of other markets (like mortgage YCs).
Here's what a yield curve looks like:
Notice a few things about it. The vertical axis is the interest rate paid and the horizontal axis is time. Notice that over the short term, money is cheap... around 1% for 1-year paper. But also notice that as we move out 10 years, the yield curve is flirting with 4%. What this curve is saying is that investors believe that 10 years from now, odds are best that bonds will be trading around 4%. The curve is now said to be positively sloped because rates today are lower than they are expected to be in the future.