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A router will block any inboud traffic where the request did not come from the lan side of the router. The exception to this is if you open any ports and allow them through. For general home use, you won't open any ports at all. For a business use, you might open the SMTP port for incoming mail if you are running a mail server, or you might open the HTTP port if you are running a web server.
As smooth said, a firewall will inspect both inbound and outbound packets to make sure nothing is connecting where it shouldn't be. For example where I work, I have an open port in the router to allow mail into my network. I can have a software firewall running on my machine to block anything coming in on that port for my machine since the mail server is not on my workstation.
If you are sure you really need a firewall instead of just your router, a dedicated piece of hardware is the best way to go.
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