the cheap $50 router you can pick up at your local electronics store
for your home broadband Internet connection is actually a pretty
It's better than nothing, that's for sure. However.....
Why or why not?
What a home level router does good is prevent external parties from initiating & establishing a connection to the resources on your network.
The reason why a home based router is less effective as a firewall is because it allows essentially all traffic originating from your network to reach out. (with the exception of a few things, like NetBIOS, etc)
Most enterprise level admins subscribe to practice of whitelisting access, meaning that unless that access has been explicitly defined the traffic is blocked.
This can be an extremely tedious task for a home network, especially if you're a gamer. You'd be surprised how many different ports and destinations come in to play.
How does Network Address Translation (NAT) increase firewall
It doesn't increase effectiveness per say, what it does do is allow you to "hide" several internal assets behind an "external" IP address.
Without going in to too much detail, there are only specific ranges of IP addresses that are routable on the internet. The assets on your internal network (ie: behind the router) have addresses that are not routable. The external interface on your router hosts the "external" IP and keeps track of who is making requests on your internal network and "translating" the traffic accordingly.