[Q] Tethering - what exactly is it?

The process of sharing the internet from your phone to another device like what you are doing is known as tethering. In your case you're making your phone appear as a dial up modem.

In Archos' case, you have some options. I don't know, but I don't believe you can tether an archos to your phone like that. I could be wrong.

As for why some phones fail to tether, it could be a couple of reasons. The most common one is that the phone is putting out an Ad-Hoc wifi signal. All android devices cannot pick up Ad-Hoc (peer2peer) signals, only Infrastructure (Access Points, Routers). There is another option for Bluetooth tethering, which I've gotten to work off my Motorola Droid, but other phones have some issues. I believe its a matter of what bluetooth capabilities the phone has (bluetooth specs similar to things like wireless audio transmitting).

I hope I cleared somethings up

Yes, your old method was basically using the phone like a modem. The tethering mentioned for android, is sharing of the internet connection the phone has.

Smartphones (and many feature phones) have an always on internet connection. It is like a broadband connection, always on and connected. Tethering basically turns your phone into a router, sharing the same connection to the internet with other devices.

The differences in WiFi and bluetooth capabilities is a concern for tethering between devices, so some people have trouble getting it to work.