Hannah Shepard is Commander Shepard's mother, if Shepard has the Spacer background. In 2183, she serves as the executive officer aboard the Alliance dreadnought SSV Kilimanjaro. One of her previous postings was on the Alliance carrier SSV Einstein.
Shepard can call her from the SSV Normandy's FTL comm unit to ask about a former comrade, Lieutenant Zabaleta. Hannah explains that as a marine, Zabaleta guarded the Einstein's CIC at the same time Hannah was on watch, and they became friends. When Zabaleta began drinking heavily, trying to handle his post-traumatic stress disorder after Mindoir, Hannah tried to stick up for him. Shepard can be sympathetic or contemptuous to Zabaleta's story after which Hannah tells Shepard to direct Zabaleta to the Veteran Affairs Office for treatment and rehabilitation.
Mass Effect 2
In 2185, she is mentioned in a news broadcast as having turned down a promotion to Admiral, as she believes serving as a Captain of a starship (now the SSV Orizaba) honors her child's memory. She later sends a message to the Normandy SR-2, titled "You're alive???", complaining that Shepard has not contacted her yet.
If Commander Shepard talked to Lieutenant Zabaleta in 2183, Hannah will send the following message to the Commander sometime in 2185.
Mass Effect 3
After rescuing Primarch Victus and bringing Garrus Vakarian aboard the Normandy, Shepard can talk to Garrus about their families and the Commander will mention that they haven't heard from their mother since the Reaper attack on Earth.
After the mission on Rannoch, Admiral Hackett will tell Shepard that he has located Hannah Shepard and has recruited her for the Crucible project. She has also been promoted to Rear Admiral in the course of the war, and is proud of her child leading the fight against the Reapers.
Mass Effect 3: Citadel
After Commander Shepard foils an identity theft attempt, a message will come in from Hannah Shepard asking the Commander to give her a call. Shepard can contact her from the apartment in Silversun Strip and the two will briefly speak about the Commander's childhood. The conversation ends with Hannah telling her child how proud she is of what Shepard has done.