R indicates the dvd is recordable (as opposed to a view only dvd). This is the most stable format for precious data you need to keep permanently.
RW - rewrittable. Like a video tape, this can be erased and re-used many times. Rs cannot be erased. This is suitable for transferring data between pcs, or recording a programme for viewing later but you don't intend to keep it.
8; 16 etc is the speed it burns at. If your dvd writer can write at 32 times play speed, it will only burn at 16 times play speed if the disk is a 16x.
Dual layer can record double the amount of information.
Good explanations here:
http://en.wikipedia.org/wiki/DVD