The First Ranger is a high position held in the Night's Watch, the group responsible for defending the Wall, and tasked with ranging beyond it. He is the leader of the rangers, only answering to the Lord Commander.
Benjen Stark was First Ranger under Lord Commander Jeor Mormont, but he went missing on a scouting mission beyond the Wall and never returned. The office was left vacant for some time during the Great Ranging, and due to the subsequent death of Mormont.
After the Battle of Castle Black, the Night's Watch had enough of a respite to hold an election in which Jon Snow was then chosen as the new Lord Commander. Jon then appointed Ser Alliser Thorne as the new First Ranger, in recognition of his long experience and his valor in the battle.