A transfer is a painted design that sometimes has texture added to it. You add them to the background of your layout to add interest & depth. You can use them to mask photos & mask or erase out part of your photo so that part of the overlay shows through.
They're called lots of different things, overlays, transfers, background fancies - they all do pretty much the same thing, but I think transfers tend to have more transparency to them.
Here are a couple of layouts from the gallery that show you what other scrappers have done with them:
I hope that helps!