The benefit for the application actually comes from the overall performance of the system. While the actual application will not run any faster because it can't utilise the second core, it will not lag behind due to CPU utilisation from other applications on your system. A good example is if you play games on the internet and you have ZoneAlarm Pro on the background. Try that on a single core system and monitor the CPU usage and you will see what i mean! hehe. On my dual core system i can run Azureus, ZoneAlarm and play a game on the net altogether without skipping a frame!
Now if you connect on the internet without a firewall, even for simple web browsing... then you get what you deserve sooner or later! (viruses, trojans, etc etc...)