The following facts, or empirical regularities, about yield curves are well-known:
Yields on bonds with different time to maturity tend to move together.
Yields on short-term bonds tend to fluctuate more than the yields on long-term bonds.
Yield curves tend to slope down when short-term yields are above average.
Yield curves are typically upward-sloping.
See, for example, Money & Banking textbooks by Cecchetti and Schoenholtz or Mishkin for more information.
The video below is an animation of every US Treasury bond yield curve from January 4, 1965 through the present. Watch the video to see if you can connect each fact with the behavior of the actual yield curve.