DSP-RPC-POSIX is a component of the C6Run project which allows you to do DSP->GPP remote procedure calls - that is, you can invoke functions/code residing somewhere on the GPP side directly from the DSP as if you were accessing a local function (there are, of course, certain requirements and restrictions).
"What functions are available on the GPP side, then?" one might ask. The answer is pretty much "everything that the hardware can do" or "everything you can do in your regular operating system" or something along the lines of that. From basic tasks like accessing the file system to more sophisticated things like sending a file over FTP, there's a myriad of possibilities.
Two reasons as to why DSP->GPP RPC is desireable would be: access to otherwise (directly) inaccessible features and being able to reuse existing code. The reason why C6RunApp exists is because it's messy to write and run code for the DSP, especially if all you want to do is try out or experiment with things (prototyping). C6RunApp makes your life easier as a DSP-side developer by offering you easy compilation/running and access to console I/O (which is actually a limited form of RPC); DSP-RPC-POSIX expands this by granting you access to virtually any existing functionality you have on the GPP side.