what he said . .

A router makes shure no traffic will be send to your internal PC's that those computers didn't request for themselfs. In that way it keeps you secure from things from the outside. And for home use mayby safe enough not to have a firewall on your local computer for that purpose.
Although there is also the thread from inside to the internet. You might have gotten a trojan, viri or somethings else. . and not know it. A router won't protect you from that. when you have a local firewall on your PC .. that will warn you if you should have one of those.
So think it will depend on the way you are surfing on the Net. And the number of people who are using the computer.
You can never be safe enough. . .but you can be to safe ad letting it prohibit your normal way to use the internet.