I think you do understand as you've described it perfectly.I don't understand, but would like to, what you mean. Small words please
Many smart phones can be set up to operate as a portable WiFi hot spot, just like a router. They broadcast a small (generally low signal strength for battery conservation) WiFi network which you can connect through if you have another device which has WiFi but no cellular access. They come with all the usual WiFi security (WEP, WPA, WPA2) and you can manage individual user accounts as well, if desired.
One major advantage of this is, if you are looking at a iPad, for instance, they come in WiFi or WiFi+3G flavours. If you get the +3G option, not only is it more expensive to buy initially but you also have to sort out another SIM card, data contract, monthly fees etc. if, however, you have a mobile which can create the portable hot spot, then you don't need any of that. You also have the advantage that you can place a phone somewhere high up to get good signal if you are in a marginal area.
If you are using a laptop or, up to now, a Google Nexus 7, then you generally don't have the option of built-in 3G, but I wouldn't (indeed, didn't) buy anything like a tablet with 3G built in anyway.
If you have an Android phone, the path to turn it on / off is Menu > Setting > Wireless & Networks > Portable Wi-Fi Hotspot, although that might be slightly different in different versions.
Hope that helped, @PaulSB, let me kow if it didn't or there's any other questions. It's a fab option which I'm sure more people would use if it was more widely understood.