A network attached storage device is a device that allows a hard drive to be shared across the network. This hard drive is NOT attached to any of your computers. It is simply made available by the NAS. This can be a convent way to add a hard drive that can be accessed by several computers on your network. The other common way to add a network hard drive is to simply share a folder on one of your computers. However, with the NAS, you do not need to keep one of your computers on at all times.
There are two types of NAS commonly available. The first type comes with a build in hard drive. The second accepts a USB or Fire wire external hard drive. The advantage to using a USB or Fire wire hard drive is that you can upgrade the hard drive if it ever were to become too small.