resolving host means taking the hostname, i.e. www.armedpolitesociety.com
, and translating it to a number.
That number is like your street address, only on the internet. That's how traffic knows how to get from one point to another.
There are special servers that translate names to addresses, and while you see "resolving host", that means your browser asked one of these special servers to translate a name to an address, and is waiting for that translation.
You could be seeing this for any specific reason, but I'd check your dial up networking config to make sure your "DNS" servers are set the way your ISP wants them, if at all. (Some are set automatically.)