A network is a set of computers and the connections between them. Blender allows you to easily harness multiple computers' processing power by setting up a "render farm" over a network.
At its core, a network is simply a collection of computers that are interconnected. The connections between these computers often allow them to transfer data; this, in turn, allows them to communicate and share files and information. For more info see the Wikipedia article on computer network.
Using Python, Blender can make use of a network for a wide range of tasks, such as distributed rendering, multiplayer games, etc.