The "Not Attached" networking mode makes your virtual machine think that there's no cable connected to its network adapter; this mode is for those times when you want your virtual machine to be completely isolated from your host PC, the Internet, other PC's in your LAN, and even from other virtual machines.
"But I could just uncheck the Enable Network Adapter checkbox in the Settings page, and it would be the same thing!" was the first thing that came into my mind when I read about this mode. Although you can achieve the same objective because your virtual machine will be disconnected from any network available to your host PC, sometimes you need to start your virtual machine without a network connection, like if you need to force an operating system reconfiguration, for example. In short, if you don't plan to use a network connection with your virtual machine, you can disable the network adapter completely, but if you just need to start your VM temporarily...