The Asari Dr. Liara T'soni is one of the chief companions you will encounter in Mass Effect 1, and into ME 2 if you purchase the DLC pack Lair of the Shadow Broker. An expert in Prothean history and archaelogy, Liara understands a great deal that is necessary for you to successfully complete your missions in Mass Effect 1. She is also a romantic interest for male and female Shepard in both games.
Liara is the daughter of Benezia the Asari Matriarch. Benezia, while alive, is a respected biotic among the asari. No one actually knows much about Liara's heritage. Unfortunately, because the other parent was also an asari however, this has led to stigmatization for Liara.
This stigma results from the belief among the Asari that nothing is gained by a "pureblood" relationship, where two asari mate with each other. Liara knows nothing about the union of her parents, but assumes that it was an embarrassing and possibly secretive relationship. She certainly does not talk much of it.
If you play Mass Effect 2, you'll notice that Liara's personality is completely different. She has become an information broker for Ilium merchants and is almost as powerful as the Shadow Broker. She's become more forceful and doesn't hesitate to use her power, intimidation, and other tactics to extract information from important people.
Knowing that Cerberus' uses for Shepard would be for their own good, she apologizes to the player for letting him or her go to Cerberus. Indeed, Liara was the one who was responsible for delivering Shepard's body to Cerberus. She wants to join Shepard but does not dare at this point for she is so bent on getting revenge against the Shadow Broker. This pains Liara and she does tell the player that she wishes she were able to go with him/her.
If, however, you choose to get the DLC Lair of the Shadow Broker, which is part of the Mass Effect 2 Collectors Edition, you will receive a more in depth view of Liara. She does join your crew after a mysterious disappearance from Ilium. Shepard has to try to "turn her" or influence her in some way as to the path she's taken. You end up in the Shadow Broker's lair, where an interesting confrontation takes place. This DLC adds a lot of depth to Liara's character and is definitely worth it for people who enjoy her storyline.
Ultimately Liara offers to help you defeat the Reapers and the Collectors through her power as the new Shadow Broker, assuming you allow her to go this route. You can also find more information in the DLC about your companions, secret missions, and other NPCs to speak to who give you important insight on Liara's motivation. You also need to have this DLC if you want to continue romancing her if you started a romance in the original Mass Effect game.