The floating leg of an interest rate swap typically resets against a published index.
Therefore, the prime factor for a constant maturity swap is the shape of the forward implied yield curves.
A single currency constant maturity swap versus LIBOR is similar to a series of differential interest rate fixes (or "DIRF") in the same way that an interest rate swap is similar to a series of forward rate agreements.
Valuation of constant maturity swaps depend on volatilities of different forward rates and therefore requires a stochastic yield curve model or some approximated methodology like a convexity adjustment, see for example Brigo and Mercurio (2006).
To take advantage of this curve steepening, he buys a constant maturity swap paying the six-month LIBOR rate and receiving the three-year swap rate.