Firstly I'd recommend reading up on DI and how it relates to Inversion of Control (IoC) over here. Basically you've most probably been using it for years and never knew the terminology. Its when some module or component of code doesn't take a reference to a resource but the resource is provided to it at runtime.
Other than the obvious design decoupling advantages, one of the most popular uses of it are in mocking - that is faking a resource - and its generally used in testing code.
So I reckon the potential for use in Silverlight is great as it allows for decoupled design.