Once upon a time, the banks used a fixing called LIBOR as a measure of the risk-free interest rate. Then the big hairy crisis came along and ate all our assumptions, leaving just the bones of the fixing (upon which everything else still fixes) and the mantle of risk-free rate proxy was passed on to a family of Overnight fixings, called Sonia, Eonia and -ahem- FedFundEffective.
Since everything (e.g. FRAs, 3m Interest Rate Futures, OTC IRS, Deliverable Swap Futures, cross-currency basis swaps, 3m-OIS basis, etc) still fixes on LIBOR (or other xIBOR depending on the currency), the questions now are:
- What do you expect the xIBOR fixing to be for any given term?
- What do you expect the Overnight fixing to be for any given term?
- How much is your CVA desk going to charge you to cover the credit risk?
So to value a forward-starting IRS, I need both an Overnight curve for discounting, but also a curve of forecasted fixings to estimate the cash flows themselves. When there was 1 curve, it was far simpler.
Summary: Once there was 1 fixing, and it was a proxy for the risk free rate, so there was 1 curve of discount factors. Now it is no longer such a proxy, but because liquid instruments fix on these other fixings, you have to build curves to work out what those fixings are expected to be as well.