A data storage device is any computing hardware that is used for storing porting and extracting data files and objects either permanently or temporarily and can be either internal or external to a computer.
CDs. Plenty of space for documents, presentation, etc. and enough room for up to 100 mp3s. You can also burn a good old fashioned mixtape onto a CD. Rewritable CDs can be reused.
DVDs. You can save files on these as you can a CD but DVDs have over five times more space. Check you computer to see if you can burn DVDs on it.
USB flash drives. Or memory sticks to most of us. Ultra convenient and nowadays the better ones have loads of memory.
External hard drives. Much the same as memory sticks but bigger with often huge capacity.