Background in a research proposal
It probably means the background relating to your proposed work. You need to explain what's been done in the field and how it's been done. Ideally you'll also show how your work will build off of previous work and advance the field. 

The point of this is twofold. First, to put your work in context for the readers of the proposal. Second, to show that you've done your due-diligence in understanding the field and won't be wasting the money in pointless or already explored directions.