the hardware firewall they are describing is prolly actually just NAT. When a remote user scans your WAN ip ports, they scan the router device instead of the client machines. If you have any port forward setup on your router, the scanner will find the open port. But if you block the port with a software firewall or disable the port forward, you will lose functionality of the service because it will drop the packets.
jeremy's right. your router isn't going to block any outbound packets. This would allow a trojan to send information it collected outside your network. you will need a software firewall for this.
cisco routers provide Access Control Lists ACLs to implement firewall technology.
Also i have run across a few hardware devices that analyze the data of the packet to make a decision on whether to allow the packet to pass or not.