The term structure of interest rates is the variation of interest rates with time — for example, it is usual for a government bond with 10 years to run till maturity to have a different YTM from one which is only one year from maturity. The term structure, especially when depicted as a graph, is also called the yield curve.
It is usual for interest rates to increase with time; the longer the time till maturity of a zero coupon bond the higher the rate of return on it. When the term structure shows this behaviour, the yield curve, when drawn as a graph, slopes upward.
A yield curve that is downward sloping is called an inverted yield curve.
There are a number of explanations for the upward sloping yield curve. The most important is liquidity preference, that investors need compensation for the potentially lower liquidity of long term bonds. Another explanation is that higher duration means greater exposures to interest rate risk and inflation risk.
The Fisher hypothesis suggests that inflation and interest rates move together, so the risks are linked.