Sarah Pearson is the mother of Vaughn Pearson. For most of his life Vaughn thought that his mother died in the accident at Paradyne as a result of his fathers carelessness.
It is later found out that Sarah was the driving force of the accident and that she lived but was stranded in the far future. Furthermore, it is learned that Sarah is an "Observer" who was charged with watching Victor Pearson in order to obtain it from him. Sarah was supposed to guide Victor in developing Paradyne industries and time travel technologies.
Sarah also worked to stop Avenir once and for all. One of the main purposes of the device Victor and Sarah created was to interrupt Avenir's plans to take over all of time and space. Sarah's device was successful in stopping Avenir and it was able to return Sarah to the present in the process.
With the vortex being closed Sarah was stranded in the present (her past) and presumably continued to live her life with Victor, helping him develop safe time travel technologies.