Typically a hardware network is made up of cables, network interface cards (NIC), routers, switches, and hubs, maybe wireless access points if it is a wireless network. A typical hardware network would be a Cisco network.
On the other hand, the software network is typically a Microsoft, or Linux network. The software controls the operations between the clients on the network and how they exchange information.
So what is server software? It is a manager. It will manage the hardware components via the network configuration, and it can manage the software sets. For example, Active directory is the server side network manager for a Microsoft domain controller. The Domain Controller is the master computer that operates and controls the network, both the hardware side and the software side.
Active directory is Microsoft Network Manager. It controls the users and computers joining the Domain, which is the group of computers. But there are other server software managers. SQL Server 2005 is Microsoft's SQL manager control program. You can write SQL programs, distribute them throughout the network, have processing occur on the client side and have the results stored on the server.
Other programs such as finance, engineering, science, accounting are typical examples of server programs that work with clients to perform operations between the client and the server.
Source: Non Microsoft Network Management Software
Microsoft Active Directory
Microsoft Sql Server