Lets say you want to make an investment with a horizon of 5 years. You have some options:
An investor can buy a bond that matures in 5 years.
Alternatively, the investor can buy a bond that matures in lets say 10 years and sell it in 5 years.
Why might an investor do this? Well, the 10 year maturity bond, in an upward sloping yield curve (and if this still holds, *goes back to your points you referenced on spot rates are maintaing the same level), will be able to sell for more than the bond maturing in 5 years (declining yield). Think of the maintaing the same level and shape as the yield curve is still positive and goes with your expectations. So riding the yield curve means an investor will buy a longer term maturity bond in the hopes that the spot rate behavior maintains the status quo.