Very often cooperative processes execute on multiple platforms making the network one big computer. Application Security is devoted to specific applications. Here you'll find issues on applications like web browsers, word processors, email clients, and IRC clients. Server Security is devoted to systems that multiple people depend upon. These include web servers, email servers, file servers, distance learning servers, etc.
Network security is oriented around the communication aspects of a networked environment.
Many applications are loaded from a server to the desktop and subsequently talk to other servers over the network. In the broader sense, the network is the collection of connecting media, connecting devices, servers, applications, and desktops and their integrated interoperation and behavior. In the meaning here, the network isn't the collection of devices as much as its the connecting medium for the devices. For the most part, this is outside user control. Ultimately, each layer depends upon other layers to make the total environment secure.