Your iPhone 3G contract was eligible for the upgrade pricing not too long ago, so you purchased an iPhone 3GS. You have your old iPhone 3G lying around the house with no purpose. Obviously, you could try and sell it... but maybe your child has been begging you for an iPod touch for Christmas. Apple wants to see these devices be re-used and not thrown into the trash, so they've outlined how to activate your iPhone (1st gen, 3G or 3GS) in the article.
It all boils down to this: never get rid of your SIM card. For the iPhone 1st generation, you have to keep the original SIM card in place at all times. Without this, it will not activate in the next software update. The iPhone 3G and 3GS do not need a SIM card installed for day-to-day use. However, you still need a SIM card for the required activation after a software update.
This differs a bit from the iPhone 1st generation: with the iPhone 3G and 3GS you can use any SIM card from your authorized carrier. Either way, it's silly not to leave the SIM card in each generation of iPhone as long as you don't need the SIM card for your new phone. Now you won't get stuck at the "Connect to iTunes" screen forever.