Well, after doing a little research I am able to answer my own questions. Two sources that helped me: the SmallNetBuilder review of the RT-N66U, which put me on to the idea that 3G/4G connectivity can be used for a full or backup internet connection, and this WiseGeek article
titled "What is WWAN?"
Here, briefly, are my answers, for the benefit of lurkers:
1. The Asus 3G/4G feature provides a way to connect your computer to a wireless phone provider's data network.
2. You would want to do this if you find yourself in a place that does not have broadband internet access; perhaps while travelling.
3. To use this feature you must have a mobile hotspot from your wireless phone service provider. You would attach the mobile hotspot to your router. However, in the typical use case you would attach the mobile hotspot directly to your computer, or you would tether your smartphone directly to your computer. You would do this with your router only if you needed to create a network.