There is DVD-R is single-writing capability. DVD-RW is rewritable capability. DVD+RW is similar to DVD-RW but better with some more features. Such as not having to completely clear the disc like a DVD-RW. DVD+R is single writing to a disc which is typically aimed at better compatability with DVD players, but there is no noticeable difference I believe. And dual layer simply means that the disc literally has two layers in which data can be burned to. This doubles the amount of space (Two the 8GB or whatnot capacity) but is also slower, and burns at around 2.4X or something like that.
You don't even really need to understand these to make a purchase. You'll probably forget anyways. It's not all that important for typical use.