If you have a small network for your home or business it probably grew up from some small number of disconnected systems. You may have—and should have—security measures implemented at each client system and, I would hope, at any servers.
But once you have a network connected to the Internet, its important to consider network-based protections. This gives you protection in case a weakness emerges on any one of the internal computers. It probably also provides protection from two different vendors, which makes it even more likely to catch rare problems that would slip through one of them. Finally, network protection gives you an element of control over your users in case you dont completely trust them.
There are two important classes of products in this regard: firewalls and antivirus protection. Actual network firewalls and network devices claiming to be firewalls are relatively common, but unfortunately network-based antivirus is still a fairly high-end product.
If you have a broadband router from a company such as D-Link or Linksys, you may have the impression that its also a firewall, but it probably isnt. These devices all provide NAT (Network Address Translation), which means that the router uses your real IP address that you got from your ISP when communicating with the rest of the Internet. Internally your computers all get fake IP addresses (probably in the 192.168.x.x range) that dont actually route out to the Internet. The fact that computers on the outside cant directly address your computers does provide some measure of protection, but its an exaggeration to call this a "firewall."
Hardware appliances that do have true firewall functionality are more expensive and more complicated to administer, but they do present a much more difficult barrier to an attacker. A talented and determined attacker will be able to penetrate the average NAT router. A true firewall performs a task called "stateful inspection," where it actually examines the packets of data moving in and out of the network, looking for evidence of attacks. For instance, if a firewall sees ICMP packets, it can look for the famous "PING Of Death" attack, which involves an oversize buffer.