Quoted from the Flex 3 Help file:
The class style used by this component. This can be a String, CSSStyleDeclaration or an IStyleClient.
If this is a String, it is the name of a class declaration in an mx:Style tag or CSS file. You do not include the period in the styleName. For example, if you have a class style named ".bigText", set the styleName property to "bigText" (no period).
If this is an IStyleClient (typically a UIComponent), all styles in the styleName object are used by this component.
The default value is null.
It is used to associated certain styles with certain components. If that certain style is applied to only 1 component than it would be normal to name it as the component to avoid confusion ( it would be cofusing if a component is named ContactForm and it's style name is "blackDog"... ok, the example might not be bright, but I hope you got the idea ). In case the style is applied to more than 1 component ( which doesn't happen too often ) than you should give it a more generalized name like "menuBarStyles" or something like that.