yield and bond valuation

The idea is basically the same as always. The market value is the PV of the future receipts, discounted at the investors required rate return. Usually we just use one required rate of return (the YTM) to discount all the receipts. However, since the receipts are each received in a different number of years (i.e. a receipt of interest after 1 year, another receipt after 2 year, etc.) it is more sensible to discount each receipt at the rate of return applicable for that time period. So for a receipt in 1 year, discount at the rate of return for 1 year (from the yield curve), for a receipt in 2 years discount at the rate of return for 2 years (from the yield curve) and so on. Because the return required changes depending on the time until the receipt (i.e. the yield curve) it make more sense to discount each receipt and the relevant rate rather than just applying one 'overall' rate.