Read original post at Sean Sexton's Blog
Once you spend some time creating a Brush in Blend, e.g. specifying the different colors in a gradient brush, it’s likely that you’ll want to use the same brush in several different spots in your user interface. You could just copy/paste the definition of the brush in XAML. But the easier way to reuse a brush is to convert it to a resource and then to reference the resource by name wherever you use it.