A router is similar to a switch, but it performs a number of useful networking functions:
It allows you to create a home network (like a switch), but a router actually separates networks allowing you to share your Internet access without being dependent on one computer's connection (unlike a switch).
You can plug a printer directly into some routers, allowing printer access to any computer on the network.
It provides built-in firewall capabilities that do not hinder network performance.
You can share your broadband connection without purchasing additional IP addresses. (Check to see if your provider allows this.)
You can also get a wireless router. It performs many of the same functions, but allows you to combine a regular network with a wireless network.