Eloise Hawking first showed up in season 3 when Desmond turned the failsafe key that made him relive the moment when he broke up with Penny. Knowing this Desmond wanted to change the course of events that led him to the island so he went in to buy a ring to propose when he met her. She was the ring lady who turned the tables on Desmonds plan when she let him know she knew what he was doing, and that if he didn't follow his original path all hell would break loose (almost like a "timecop" trying to fix the course of events).
We didn't see her again until she showed up this season and was infact Daniel Faradays mother (the young angry British girl named "Ellie" on island) we also learn that she and Charles Widmore had a fling and is infact Daniel's father.
