wot 'e said.
The NAT firewall will stop the person who tries to connect to your machine from outside, to do nefarious things. That's good.
It won't stop the smarter hacker who conceals some software on a website. You visit the site, you download the software, it installs on your PC, and you know nothing about it.
It will then do whatever it's designed to do - collect your internet banking login and account details and send them to base; collect your address book ditto; wipe your hard drive on April 1; send 20 million spam e-mails from your PC...
I've seen the logs of the AV on my machines, and seen the stuff arrive and get zapped. When I changed from AVG to Avast on this machine, it found a couple of dozen cookies that it reckoned were slightly dodgy - not dangerous, just dodgy.
You can't be too careful.