Quite a lot of the time you will have a dynamic ip, this will change IP when you reconnect to your ISP
So say your IP is
155.262.26.00
It could change to
155.262.27.00
So if the forum ban
155.262.**.**
(* = WildCard)
Then they could be stopping other peoples internet connections, so forums usually ban the IP account you last logged onto because this is what most forum softwares work
This is because your ISP will usually give you a range of IP's for your households, because it is harder for them to give you a static IP. A Static IP never changes, this is usually what businesses will have.
Thats pretty much the basics of it.