I was teaching still at the Albert-Louis, and Tom sent me an e-mail asking me the manorial records for Oberhochwald to find. These were supposed to be in our University collection. I replied, Was that a personal supposition, a material supposition, or a simple supposition? And Tom responded <LOL?> because he did not understand the joke. He supplied a list of key words and a request to search our manuscripts and incunabula for references pertaining to Oberhochwald, which I suppose was fit punishment for my attempt at medieval humor. Supposition theory is not much funny, especially as we don't really know what they meant by it all.
I don't think it's quite correct to say that "we don't really know what they meant by it all" (it's not like the theory of supposition is as obscure to us as, say, the theory of obligationes), but there is indeed some dispute about it. The standard view is that supposition theory is a theory of reference. That this is the standard view is in great measure due to Peter Geach. Gyula Klima has done some interesting work showing that one can actually get pretty far with the standard view; this paper (PDF) gives some idea of it. Catarina Dutilh Novaes, however, has written some interesting and excellent papers arguing that the standard view is somewhat off, and that supposition theory should be seen as an apparatus for the semantic analysis of sentences, a means by which one might uncover ambiguities and clarify them. This one (PDF) is a good place to start in order to get the gist of her argument.