The rank was only used in the German army's heavy artillery branch (Fußartillerie) before 1919 and commonly established with the founding of the Reichswehr. Translated as "senior lance-corporal", in World War II the rank was normally given to soldiers who had command over small squads or to those soldiers who held the rank of Gefreiter and had performed a significant feat of achievement. An Obergefreiter was not considered a non-commissioned officer (Unteroffizier).
In today's Bundeswehr, every Gefreiter is normally promoted Obergefreiter after six months. The NATO-Code is OR-3 which would make Obergefreiter the equivalent to private / airman / seaman first class in most forces or, e.g., lance corporal in the Australian/New Zealand Forces. Like all enlisted personnel in the German Bundeswehr, soldiers of this rank have no military authority over lower ranking enlisted personnel (for instance Schütze or Gefreiter), except given by a higher rank.
In the Swiss Armed Forces the rank of Obergefreiter (short: Obgfr) was introduced after a long debate on 1 January 2004. They are specialists, who take over tasks of responsibility or hold the position of a group commander.