Basically your IP address will be on your machine and the ISP server's so that they can talk to eachother?

No, if you want to change your addy you have to reconnect.

Your ISP has a "block" of addresses.............rather like banks have blocks of sort codes...........the first numbers identify the ISP, the later ones identify your connection at that point in time.

Subnets are the middle bits of the code..........your ISP has numerous servers, sites, and addresses to hand out.............these are divided into subnets.

Hope that helps, no doubt an expert will fill you in with the technical stuff.

Cheers