A writable (or re-writable) DVD is essentially just a higher density/capacity version of a CD. It can be used for the same files etc and movies that you can put on a CD/R but you can get lots more on it. You can get 700MB on a CD and 4.7GB on a DVD. For both formats R is write once, RW is re-write.
DVD writers and DVD roms can usually read CDs, but not vice versa. Set-top DVD players can read DVDs and CDs and often CD/R and CD/RW. Audio CD players can generally only read CDs, and then only when recorded in audio CD format.
If that's not complicated enough, there are different DVD writable formats eg DVD+R and DVD-R. There are re-writers which will write both standards (and read both) but those set-top DVD players which will read writable DVDs will usually only play one type.