....is a way of visually expressing the return available from bonds of the same type but different duration
The yield curve is a chart of the yield to maturity (the more usual name for 'return' when used for bonds) of bonds of similar type, but varying lengths to maturity. A yield curve is drawn on a graph with a horizontal axis of time to maturity of the bond and a vertical axis of yield.
In normal times investors will seek a higher yield for tying up money in a long term bond than for a short term bond, to reflect the increased level of uncertainty of future interest rate movements and the outlook for inflation; or, to put it another way, the longer period before certainty prevails by repayment at par (i.e. on the due date for the due amount). Thus a ‘normal’ yield curve would slope upwards.
A downward sloping yield curve is described as ‘inverted’. This is unusual, as it indicates a market expectation of decreasing spot yields (so investors are prepared to lock in to yields-to-maturity which, while worse than today’s spot yields, are better than they expect to get if they delay).
Note that movements in the yield are inversely proportional to the market price. Higher demand for a bond drives up the market price and results in a decrease in the yield and vice versa. Market commentators will frequently refer to falling bond prices as ‘an increase in the yield’.