A bond is a strong attachment or connection between two or more people which can often last for life. In human relationships they say the strongest bond is that of a mother and her child. A bond can develop from love, affection and trust or out of shared experiences,
But in the case of vampires 'bonded' usually refers to a 'blood bond' which comes from someone drinking the blood of a vampire at least three times after which they are totally enthralled by the vampire and love them as much as they are capable of loving anyone and will do anything the vampire asks them to. This bond can happen between two vampires or between a human and a vampire.