A yield curve shows the relationship between the yield on securities and their maturities (how long it is until they can be redeemed at their face value).
Generally, in developed countries, the curve of the yield plotted against maturity will slope gently upwards, reflecting the fact that investors expect to be paid more interest for locking in their investments for a longer period than a shorter one. The higher the rate they expect, the steeper the curve will be.
The shape of a yield curve is, to a degree, seen as a predictor of the future. A downward sloping (or ‘inverted’) yield curve suggests that investors expect long-term interest rates to fall, and is often taken as a sign that an economic downturn is on the way. An upward-sloping one suggests the opposite.