An Executor is named in the last will and testament of a decedent. If an Executor is not named, the court will appoint an Administrator with will annexed.
To ensure an Executor carries out their duties, the court might require the Executor to get bonded with an Executor Bond.
If the will states a bond is not required, the court still might require one. Common situations where this might happen include if the Executor or Administrator with will annexed is a non-resident of the state having jurisdiction over the estate. (See more: Does Your Will Executor Need To Be Bonded?)