A personal recognizance bond is an obligation freely entered into before a common law court to take up and execute some duty, according to Dictionary.com. This specified act is often simply to return to the court at the appointed time to face charges and is essentially a promise that the defendant has to make in lieu of posting large sums of cash as a bond.
Personal recognizance is a common legal concept in the United States, United Kingdom, Hong Kong and Canada, according to Wikipedia. It always takes the form of the person before the court recognizing a debt to the state and agreeing to behave in a specified way in order to repay that debt.
Wikipedia states recognizances are most often encountered regarding bail in criminal cases when the defendant agrees to return to court for trial on a particular day in order to avoid further imprisonment pending trial. Another common recognizance is to keep the peace, in which the defendant acknowledges a criminal debt to the state, usually for a minor infraction, and the court discharges that debt on the condition that the defendant simply abstain from violating the law going forward.
Defendants released under such circumstances are said to be released "on their own recognizance." Sometimes, the term is abbreviated RoR, for "released on recognizance." More commonly in the United States, the term will be further abbreviated to "OR."