If your DIR-825 is facing the world (ie: gets a public IP from your service provider,) having the firewall turned on is not only good practice, but an absolute necessity. NAT does not protect you from would-be hackers. The purpose of NAT is to allow more than one device access through a router (in this case to the internet cloud) without having to assign each device a public ip address (there just aren't enough in IPv4 to do that.)
NAT does offer limited security in that the router will not accept incoming data connection requests if an outgoing session hasn't already been opened. But that's it.
There are two types of firewalls (the 825 has both..)
1) Port forwarding/blocking (depending on the vendors choice of words)
-- Allows you to prevent all incoming traffic that hasn't specifically been approved, from entering your internal network.
-- Does NOT necessarily hide your network from the world though.
2) SPI (Stateful Packet Inspection)
-- Firewall looks inside each incoming packet and using a set of rules and algorithms (way to complicated for my brain to understand) will drop packets it determines to be harmful.
-- SPI, I believe, should be turned on by default on the 825 b. If not, TURN IT ON!
If anyone is interested, I can put together a quick guide on hardening your network with the DIR-825 b. If interested, please fill out this short poll at
http://links.waffull.com/dlink