a router is an example of a gateway
like for example, if you have dsl or cable internet at home, there's ususally a modem, well that modem can your your gateway to the internet.
for example, if you have windows computer, go to the DOS command and type: ipconfig you will see something like this:
Microsoft Windows [Version 5.2.3790] (C) Copyright 1985-2003 Microsoft Corp. C:Documents and SettingsAdministrator>ipconfig Windows IP Configuration Ethernet adapter Local Area Connection 2: Connection-specific DNS Suffix . : IP Address. . . . . . . . . . . . : 192.168.1.102 Subnet Mask . . . . . . . . . . . : 255.255.255.0 Default Gateway . . . . . . . . . : 192.168.1.1 Ethernet adapter Local Area Connection: Media State . . . . . . . . . . . : Media disconnected C:Documents and SettingsAdministrator>
as you can see, my gateway is 192.168.1.1 which is the ip address of my wireless router at home