Home Networking 101
A hub is typically the least expensive, least intelligent, and least complicated of the three. Its job is very, very simple: anything that comes in one port is sent out to the others. That's it. Every computer connected to the hub "sees" everything that every other computer on the hub sees. The hub itself is blissfully ignorant of the data being transmitted. For years, simple hubs have been quick and easy ways to connect computers in small networks.
A switch does essentially what a hub does, but more efficiently. By paying
attention to the traffic that comes across it, it can "learn" where particular
addresses are. For example, if it sees traffic from machine A coming in on port
2, it now knows that machine A is connected to that port, and that traffic to
machine A needs to only be sent to that port and not any of the others. The net
result of using a switch over a hub is that most of the network traffic only
goes where it needs to, rather than to every port. On busy networks, this can
make the network significantly faster.
A router is the smartest, and most complicated of the bunch. Routers come in all
shapes and sizes, from the small four-port broadband routers that are very
popular right now, to the large industrial strength devices that drive the
internet itself. A simple way to think of a router is as a computer that can be
programmed to understand, possibly manipulate, and route the data its being
asked to handle. For example, broadband routers include the ability to "hide"
computers behind a type of firewall, which involves slightly modifying the
packets of network traffic as they traverse the device. All routers include some
kind of user interface for configuring how the router will treat traffic. The
really large routers include the equivalent of a full-blown programming language
to describe how they should operate, as well as the ability to communicate with
other routers to describe or determine the best way to get network traffic from
point A to point B.