A device is a hardware component with a distinct purpose. For example your mouse, keyboard and monitor are devices. Under Linux, devices are assigned a special file and listed under /dev.
Main article: block devices
A block device is a device organized in blocks, typically a hard disk or CD. It differs from a character device by the possibility of seeking forward and backward. Hard disks typically have a device file like /dev/sda or /dev/sdb.
A character device is a device that delivers characters, but you cannot seek on. Examples include the keyboard and /dev/random.
A network device like your network card does not have a representation in the /dev folder.
What to do with a device
Formatting means making a file system on a disk erasing all data. You can make different file systems under Linux, one of the most prominent ones being ext4. To make this, in this example on /dev/sdx1, open a console and enter
A hard disk with a file system on it can be mounted like this:
mount /dev/sdx1 /mnt
This will use the partition /dev/sdx1 and mount it to /mnt