Windows Network Discovery is a robust way of discovering devices and their capabilities on a network. It scans the network for any used IP addresses, then uses Windows Domain Services, DHCP, DNS and SNMP to attempt to discover the capabilities of each device found.
Due it its ability to determine capabilities of each connected device, Network Discovery can create topological maps where, under most situations, routers, managed network switches and other devices can be placed in a valid network map, showing the intricacies of your LAN.
Network discovery is a useful tool which allows you to easily see what is on your network. However, this should never be used in a hostile environment since it also allows (on Windows) other machines do discover information about your workstation.
With Network Discovery off, other machines can still see that a particular IP address is in use, but not tell that it is, say, a Windows 8 machine with the name MyComputer. The information about your particular machine will be limited to what can be found from other devices, such as routers, DNS servers or DHCP providers.
In a secure environment, say a well protected Local Area Network (LAN) with good anti-virus installations an a protected router, Network Discovery can be a useful tool However, in situations where security is not absolute, you must decide whether you want it enabled or not.
This is very dependant on which version of Microsoft Windows you are using, but basically, you must Change advanced sharing settings in the Windows Network and Sharing Center.
Performing a https://duckduckgo.com/ search for the phrase windows network discovery turn off should result in a good answer for your particular machine.
Note: the previous link will actually execute the query. We prefer duckduckgo.com since it returns more consistent results than other search engines like Google or Yahoo.