There are two types of routers which are, wired and wireless. A wired route will be connected through a modem to the internet.
The local area computers are connected using Ethernet cables to the router. If a single computer is to be connected to the internet, then the cable modem can be considered to be a router also. The router allows multiple computers to communicate with each other, and to communicate to the internet, sharing a single internet connection.
Broadband means either having a cable modem or a DSL connection. As, these are high-speed connections that connect your computer or computers to the internet, they are referred to as broadband. There are two types of broadband routers that are used in a network.
One is the wired router that has been described. The other type of broadband router is the wireless router. This router looks like the wired router the only difference is that in size it may be smaller than a wired router, and will have one or two antennas on it. A wireless broadband router can also be a mixed router and may have some Ethernet cable ports on it.
This router allows computers to be connected by Ethernet cables and wireless computers can connect via the router to the internet and to other computers on the network too. Wireless routers use an encryption to disallow eavesdroppers from accessing the network too. Other than routing data packets on the network, and between networks, there are broadband routers that can be setup as firewalls and DHCP servers.
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