NAT is Network Address Translation. Basically it's how you can have multiple computers/playstations/xbox's all on the same Internet Connection.
Your Internet Provider gives you an address of aaa.bbb.ccc.ddd (where each of those represent a number between 0 and 255). Your router then takes each of your computers and gives them an internal address - usually on the 192.168.ccc.ddd address range.
Your playstation has one address, your computer another, and so on. Well, when COD:MW2 from another playstation tries to send a request to yours, it sends it to the public address (aaa.bbb.ccc.ddd) - your router doesn't know who it goes to, so it discards it.
The way to get around this is to tell your router that all requests that are on certain ports (COD:MW2 uses UDP 1500 (outbound), UDP 3005 (outbound), UDP 3101 (outbound), UDP 28960) to go to only your playstation.
To do this though, you need to know the internal address for your playstation.
1. Power up the PlayStation 3 without any disc in the drive.
2. Once the PlayStation 3 operating system has loaded, select Settings.
3. Once you are in Settings select Network Settings.
4. When the Network Settings list appears, select the first option which is titled Settings and Connection Status List.
5. The physical address will be listed under MAC Address.
Write down this physical address.
Go to your router with a web page. Usually will be 192.168.0.1 or 192.168.1.1 or 192.168.10.1 depending on who makes it.
There will be a place to put in these paths; unfortunately, there are too many possibilities to list. Go to your router manufacturer's website to get instructions or your manual.
Oh, and be very careful in there if you don't know what you're doing - screwing that up can cause a lot of headaches.
Good luck!