This kind of flash diffuser produces a "bare-bulb" effect. It's not like a softbox or umbrella, which works by effectively making a larger light source. Instead, it makes the light from your flash less focused, so it's diffused by bouncing off walls and other objects.

Normally, a hotshoe works like a spotlight — it focuses its output in a cone. That's good for efficiency, but makes the light rather uni-directional and harsh. A bare bulb, on the other hand, scatters light in every direction. From the point of view of a subject, it's still one source, but the scattered light also bounces around the room, providing softer fill light.

Many people try to use this type of push-on diffuser to improve the appearance of flash when shooting in large spaces or outdoors. _This will lead to disappointment._ The little bit of plastic doesn't do much but cut light output in this case.

The Sto-Fen Omnibounce is one of the more popular brand-name pieces of push-on plastic, and they have a [diagram of the effect](http://www.stofen.com/info/howitworks.asp) on their website. Note the bouncing arrows — that's critical, even though they don't really explain that every well.

Of course, a real bare-bulb (also called "bare tube") flash just doesn't have a focusing reflector in the first place. This is a lot more effective than having the reflector and sticking a little white plastic box on top. I'm not aware of any hotshoe units made to work this way (short of somewhat-dangerous D.I.Y.),  but many studio lights ([like this](http://www.adorama.com/QTQFT5DR.html)) are made to easily support this configuration.