What part of a computer is used to store data?

For the short-term, specifically while you have the computer turned on, information is usually stored in RAM, which is fast, but volatile - it loses its contents when you turn the computer off.

For the long-term, information is stored in some non-volatile memory; traditionally, diskettes or hard disks have been used for this, but in some cases they are being replaced by flash memory. For instance, Cisco routers and switches use flash memory instead of a hard disk; so do the laptop computers produced by the OLPC (One Laptop Per Child) foundation.