The Remember Position checkbox is a part of the Playback settings.
Definition
This option only controls what happens when a shot has been playing in Live and you transition to another shot which does not contain the same media.
Controls whether the shot remembers the last position it was played the media.
When Remember Position is on (checked)...
When Remember Position is on, the last position is remembered. When the shot becomes live again, it will start playing from that position.
When Remember Position is off (un-checked)...
When Remember Position is off, the position is not remembered. When the shot becomes live again, the media will start playing from the In Point.
Default
This checkbox is on by default; the position will be remembered when the shot is no longer live.