A vampire coven is a vampire family, or a vampire pack if you will (but you're most likely to get bitten if you use that word.) They are simply vampires that live together and try to do so in relative peace.
Some covens are friendlier than others and really are like family to each other. Other covens have members that tend to keep to themselves and really just view the coven as a place to live. In either case, there is always a sire of the coven who is deemed to be the head of the coven or the ruler of the coven. Covens can also be for only a certain number of vampires, or they can be for larger groups, such as an entire city. All covens however, will have their own rules to abide by. Even though rules will vary from coven to coven, they all generally cover four topics: joining the coven, eating, creating vampires, and general behavior within the coven.
There aren't really any ranks in vampire covens, except for the sire. Although each vampire will have their own strengths and weaknesses, one is not necessarily better than the other. Some covens do work on a superiority system, where decisions that need to be made will be done so by those who have been there the longest. But generally, everyone's on equal footing within the coven.
Some vampire covens think it's disdainful to eat anything other than human blood but some covens mix in animal blood along with their human diet. Most covens though do feast on humans and aren't as nicety-nice as they are in the Cullen household. Choosing prey and covering up the meal though must always be done so very carefully. Leaving dead bodies in your path and always having screaming humans fleeing from you is a sure way to get the coven noticed.
In the same kind of thinking, vampires generally aren't allowed to act too recklessly within their coven. This is anything that would draw attention to them such as running a full street in half a second, not moving for a very long time in the presence of a human (who may think it odd), or leaving traces of blood on the clothing are all behaviors that could be considered reckless and could get a vampire asked to leave any coven.
The rules regarding the behavior of the vampires within the coven generally refers to how vampires treat the other vampires within the coven. Coven members are never to turn on each other and try to kill each other. No ifs, ands, or buts about it. In almost all covens, if this happens, the vampire that first attacked is most likely to end up dead. Even in covens where the members aren't super-close to each other, they still must remain respectful at all times.
That's just a brief overview of how covens work. Individual covens generally have a fairly lengthy script of what's allowed and what's not allowed in their coven. And if any of their rules are disobeyed, being thrown out is the best thing that could happen to you!
Haunted Mansion created by Arlen Nielsen. http://www.fabmedia.com