Just as adding more flashes will give you exponential lighting possibilities, working with light-modification tools will give you even more ways to control, shape and build your light. These tools are important because your flash is a highly directional light source. When used without any modifiers, a flash produces scenes with very heavy contrast. Your subject is lit from a single direction while the rest of the scene is dropped into shadow since the camera meters for the flash burst.
The most popular diffusion system is the softbox, which offers a front panel of white see-through material on a housing that usually includes a reflective interior for channeling as much light spill from the flash forward as possible. The result is softened wraparound light that's very flattering for portraiture, much like natural daylight through a window on a cloudy day. Many softboxes are available with removable interior baffles for diffusing light further. Octaboxes offer a similar construction with a wider, more circular shape for a larger spread of light and rounder reflected catchlights in the eyes.
Domes are great diffusion solutions for on-camera flashes during events because they soften the highly directional output, and produce candids and portraiture with a more natural overall light spread that's similar to bouncing the light from a nearby wall or ceiling. They don't channel light forward, however; light rays are distributed along the circular circumference of the globe and become more omnidirectional. Domes can reduce light output quite a bit and are better for working at close distances.