Liara: The Observer
On Illium, you will meet Liara, who wants you to hack some terminals and send her the data.
Bring a tech specialist with you and head over to the Transportation area, where you go to begin the Recruit the Justicar mission. There, you will find three terminals which can be hacked. Once you hack each terminal, a countdown will begin. In the bottom-right area of your screen, you will find a distance meter, which will decrease as you approach the next terminal where you can upload the data.
Repeat this two more times and return to Liara. She'll give you The Observer quest, in which you need to hack terminals to gain information and determine the identity of the Observer. Most are just outside her office in the marketplace area, although one is located at Eternity upstairs.
Once you've hacked all five terminals (and not before), call Liara. Choose the middle-right dialogue option — that none of these people fit the description.
Once you do, you'll discover who the Observer really is. Return to Liara and end the quest.