A more thorough explanation:

Definition: An oath taken to renounce or give up something, usually by swearing an oath.

Example: Abjuration of the realm was an oath taken by a malefactor who took refuge in sanctuary. The coroner would come and offer the refugee a choice between submitting to trial or abjuring the realm. If the refugee chose the latter, they would leave England dressed as a pilgrim and bound by their oath never to return. Their lands and chattels would be forfeited, and if they returned, they would be treated as an outlaw.

Another example: In English law, the oath of abjuration was an oath renouncing all right of descendants of a pretender to the Crown. This oath was taken to show loyalty to the reigning monarch and to prevent any potential claim to the throne by the pretender's descendants.

These examples illustrate how an oath of abjuration is a solemn promise to give up something, whether it be a claim to the throne or the right to return to a certain place. It is a way to show loyalty and to avoid punishment for wrongdoing.