A 2501 Cisco router is considered for the purpose of understanding typical Cisco router interfaces. Please note that this is an entry level router, and the interfaces may be quite complex for high end routers.
2.1 Interfaces Explained
Console port: This is used for connecting a console to the router. The console terminal will have direct connection to the router, and you will be able to access all router interfaces and configure the same. When you receive a new router, you need to use the console port to configure it.
Auxiliary port: Auxiliary port is used to access the router remotely using a modem. For this purpose, you need to have the auxiliary port configured before hand.
Synchronous ports: 2501 has two synchronous ports as shown in the figure. These ports can be used to connect to any serial line.
Ethernet AUI port: This port is used for connecting to the LAN.