Cameras need light to create images, and when ambient light is low, an on-camera or external flash comes in very handy. As in so many things in life, though, sometimes the solution--in this case, the flash--creates a new set of problems.
Light from a flash can be harsh and overpowering and unnatural, adding hard shadows to subjects that don't need them. In the case of portraits, flash often blows out some details, reveals unpleasant minutia, and as we already mentioned, forces ugly shadows into some images.
To avoid these kinds of problems, you need more diffused light, like the kind you see outside on a cloudy day. But how do you soften light from a flash? Well, you can buy a pricey diffuser, or you can simply make your own.
For more on flash diffusers, please read Flash Diffusers 101.