A personal representative of an estate is an executor, administrator, or anyone who is in charge of the decedent's property. Generally, an executor (or executrix) is named in a decedent's will to administer the estate and distribute properties as the decedent has directed. An administrator (or administratrix) is usually appointed by the court if no will exists, if no executor was named in the will, or if the named executor cannot or will not serve.
This information is found in Publication 559, Survivors, Executors and Administrators.