What A Collar Means
Collaring is when a Dom claims a sub as their own. This can be literal--actually placing a collar around the neck of the submissive--or it can be figurative and be an understanding between the people involved. Often the literal option is chosen, because the collar is recognized within the community as a mark of ownership.
Collars are, again, a mark of ownership. Collars mean that a Dom has exclusive rights to the sub that is wearing their collar, and that he or she makes any decision that affects that sub. In some communities it is accepted that a person will check with the Dom before any interaction, even conversation, with the submissive. Most communities are not this formal, but that doesn't mean that the Dom does not have complete control over what is done to the sub that is wearing his or her collar. To touch, molest, use, or require something of a collared submissive by someone who is not their owner and is not acting under the owner's instruction is considered unforgivably rude. It is valid and acceptable for a sub to ignore an order from a Dom who is not their owner or is not sanctioned by their owner.
The collar means, besides ownership, that the Dom/me has agreed to the care and protection of the submissive. The education, behavior, nurturing, and punishment of the submissive all fall to the Dom who has placed the collar. If there is a problem with the sub, or if there is something desired of the sub, their Dom should be consulted first. Never assume you have any rights to a collared sub that is not your own.
Collaring is a serious step. By placing a collar, you are agreeing that this person is in your care, or you are agreeing that you will surrender your personal power to this person for as long as you wear their collar. It is a step that should be weighed carefully and not jumped into blindly. Make sure, before the collar is placed/accepted, that you and your Dom/me agree on what that collar means to you both.