The Executor/Executrix (male/female) is an individual, corporation, or institution that you name specifically in your Will and who is responsible for administering your Estate. In short they carry out your wishes including distribution of assets to beneficiaries. You may name more than one Executor/Executrix.
The duties of an Executor/Executrix will vary depending on how complex your Estate is but they include assembling and categorizing the value of assets, protecting such assets until distribution, obtaining probate from the appropriate court, and administering and distrubuting the Estate including closing bank accounts, paying off debts, filing tax returns and obtaining tax clearance certificates, etc.