Administrators can ban players from their servers if they see fit. It's an extreme measure but it's their server so why put up with disruptive, abusive or cheating players? Bans can be applied to individually named players and/or their IP address and/or whole ranges of IP addresses. Bans can have whatever duration the administrator deems appropriate, ranging from minutes, through days, to permanent.
Don't worry though, play nice and you won't be banned!
Caught in a foreign ban
If you try to join a certain server but it refuses you and you know you have not been banned from that server, then you're probably caught in a ban that was thought to get rid of someone else. This is mostly caused by ranged IP- or host-bans (like 12.34.*.* or *.provider.net); although this is a bad idea to ban it happens often enough to get people caught in such a ban regularly.
Way out: Contact administrator
The most efficient way to get out is to contact an admin or cop with unban permission on the particular server, best would be to contagt the person running the server. Do this via a PM on the BZBB or try to find this person in game.
A lot of servers also use a so called "whitelist" which prevents registered players from being banned (+ANTIBAN), you could also ask to get on the whitelist for this particular server in case it's got one.
Way out: Changing your IP
This isn't the master solution but something you should at least give a try. Most people are given another IP every day when they connect to the internet, so you could have bad luck and get a banned IP for a server. The solution would be to simply disconnect your router/modem from the phone/DSL line and plug it back in after waiting a second or two. You will then be given a new IP and you've got a chance to be out of the ban.
Doing it wrong
You will probably not be heard and ignored if you start topics somewhere in the BZBB asking how a ban coulb be 'undone' or messing with random people on the IRC or other servers. Additionaly forum topics regarding unban-requests get deleted very frequently.
Caught in a purposed ban
You misbehaved and got banned. If you're a known troll your chances to be unbanned are almost zero. If you just had an accidently freakout you could try contacting the server owner, excuse for your behaviour and ask to be unbanned nicely, they'll probably accept it.