I read that a three blade can improve climb performance and decrease noise. How does that work?
At the absolute simplest, compared to a two-bladed propeller, a slightly smaller three-bladed propeller can produce more thrust at a given RPM, improving climb performance. Because of the smaller diameter, the propeller tips actually travel slower than the equivalent two-bladed design, reducing noise inside and outside the airplane.
Hartzell Propeller has a great set of technical answers about propellers. Their explanation of why more blades produces less noise is pretty good:
A 2-blade propeller produces two pressure pulses per revolution, where a 3-blade propeller will produce three smaller pulses per revolution (for the same amount of total thrust) which is inherently smoother and therefore quieter. The 3-blade propeller will generally have a smaller diameter than the 2-blade propeller that it replaces, which also reduces the tip speed and noise.