Application static resources are used to declare instances of objects that should be alive and reusable throughout the whole life of an application. Usually as static resources are declared such things as styles, templates etc. Thus they can be used multiple times from multiple places within your Silverlight application.
Xaml
<Application xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
x:Class="SnackBites.App"
xmlns:local="clr-namespace:Bomb">
<Application.Resources>
<Style x:Name="simpleStyle" TargetType="Button">
<Setter Property="Content" Value="Static style content"></Setter>
</Style>
</Application.Resources>
</Application>
Note that for each resource you declare x:Name or x:Key should be specified!
That's it!