router5 is part of a new generation of routers: instead of rendering "views" or "pages", router5 outputs its state. The main idea behind router5 is to treat routing state like any other application data or state.
"Traditional" routing has been heavily influenced by server-side routing, which is stateless, while client-side routing is stateful. Watch my talk at ReactiveConf 2016: "Past and future of client-side routing", it gives a great overview of what routing is, and what router5 does:
For more in-depth description of router5, look at Understanding router5.