Background in a research proposal in a project proposal, I am asked to write a section where it I will describe the background. I am not sure this means my research background so far and connection with the proposed project, or general background of the field of research. It is for a postdoctoral position.

Thanks
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.