Forward Curve

This is the cost of borrowing when you are making payments in the future.
Also known as Forecast Curve or Future Curve or Hedge Curve
Also known as implied forward rates, nominal forward rates

A forward rate is the implied interest rate that would be used for an investment in the future.
The forward (or forward-forward) yield curve is a plot of forward rates against term to maturity.
Implies the interest rate that would be used on a date in the future

rate between two future dates

Theoretical Curve

These are "implied" forward rates.
The forward yield is the interest rate implied by a zero coupon rate.
Forward rates are a type of market view on where interest rates will be (or should be) in the future
Forward rates are the markets expectation of future rates.
Forward rates are not a prediction of future rates.

The forward yield curve is a plot of forward rates against maturity.
The forward yield curve is the interest rate implied by the zero coupon rates for period of time in the future.

These are used to work out the cash flows in an interest rate swap

Assumptions

1) Markets should be arbitrage free (ie you cant make money unless there is a risk involved)
2) A 1 year investment in treasury bills should produce the same return as 2 consecutive 6-month investments in treasury bills.
The 6-month rate you would get four 6-months periods from now is know as the 2 year forward rate denoted:

Relationship between Spot and Forward

There is a mathematical equivalence between spot rates and forward rates.
We can see that the spot yield is the geometric mean of the forward rates.