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Daenerys is the last surviving daughter of the Targaryen family after Robert Baratheon conquered Westeros. Along with her brother, Viserys, she is exiled in the land across the Narrow Sea.
Background
Daenerys is the only daughter and youngest child of King Aerys II Targaryen also known as the Mad King. She was born on the island of Dragonstone during a storm and for this reason is sometimes referred to as Daenerys Stormborn.
Her mother, Rhaella died during childbirth and most of her family died during the Sack of King's Landing. This was a deadly assault by House Lannister in which her father and his followers were killed.
When she was a baby Daenerys and her brother Viserys were taken to the Free Cities by loyal retainers. Their followers spent years trying to gain support to retake the Iron Throne to no avail. The siblings were given sanctuary by Magister
Illyrio Mopatis.
Major Plots

Daenerys and her white horse
Encouraged by her brother Daenerys is married to Khal Drogo, the leader of a group of Dothraki people. Viserys plans to use the khalasar (Khal Drogo's army) to invade Westeros and although Daenerys is apprehensive, she has no choice but to wed him. When she is married Daenerys receives gifts, including three dragon eggs that have turned to stone from Magister Illyrio. A knight from Westeros known as Jorah Mormont gifts her books about the seven kingdoms and offers her his services. Drogo gives her a white horse and has sex with her, although she cries and seems fearful.
Drogo and the khalasar march for several months and Daenerys begins to adjust to her new life. She asks her new servants who were formally prostitutes for advice on sex and how to please her husband. After using her new found sexual confidence on Drogo the pair form a close bond and she becomes pregnant, announcing that she believes the child is a boy. She also uses her new found confidence to begin standing up to her brother.
The khalasar reaches the Dothraki city of Vaes Dothrak. After inviting Viserys to dinner and offering him clothes he rejects

Daenerys eats a stallion heart
Daenerys offer, striking her in the face. She retaliates by hitting him with a gold belt and announcing she will have his hands removed if he strikes her again. During this time she also eats the heart of a stallion in front of the Dothraki wise woman and it is predicted her son will be, the Stallion Who Mounts the World, the khal of khals who will unite the Dothraki into a single horde that will overrun all the lands of the world. Viserys storms in demanding that he be given payment for Daenerys. Drogo then executes Viserys by pouring molten gold on top of his head.
Daenerys still tries to convince Drogo to continue the invasion so their son can sit on the Iron Throne. He refuses as Dothraki never cross the sea as their horses cannot drink its water. She is almost poisoned by an assassin of Robert the current King and Drogo changes his mind in anger, announcing that their son will mount the Iron Throne.

Drogo and Daenerys
The khalasar march to Lhazar, to obtain slaves and loot to sell so they can raise funds to obtain the throne. Daenerys is shocked by what she sees and convinces Drogo to treat the woman they enslave better. Drogo slays one of his followers, Mago, when he disagrees with the decision. Although he is victorious Drogo receives a wound to his chest. One of the enslaved women, Mirri Maz Duur, treats the wound.
The Khalasar continue to march, heading south to a great wasteland. Drogo falls from his horse as his wound has become infected. Durr continues his treatment, but believes that the wound has become fatal. Daenerys convinces her to use blood magic to save Drogo, although the Dothraki object. Ser Jorah defends Daenerys from, Qotho, a bloodrider who objects. She is injured in the battle and goes into labor. When the Dothraki midwives refuse to treat her Ser Jorah takes her to Durr to give birth.

Daenerys with a newly hatched dragon
Daenerys loses the baby, but Drogo is saved. The khalasar have scattered leaving only a few behind. Daenerys is shocked to find that she unwillingly sacrificed her baby to save Drogo and that he has become and empty shell. She smothers him with a pillow to end his misery. He is then burned on a funeral pyre that Durr is tied to. Daenerys Dragon eggs are also placed on the pyre and she walks into the flames to die with her husband. The next morning Daenerys sits in the ashes naked with three small dragon perched upon her. The remaining Dothraki and Ser Jorah fall to their knees, proclaiming her as their Queen.
Personality and Traits
Daenerys is very timid due to her brothers cruel treatment as well as the separation from their homeland. She is easily manipulated by her brother and marries Drogo due to his demands. After her marriage to Khal Drogo she becomes a khaleesi and realizes that she now has power. This leads to her gaining more confidence as well as standing up to her brother.
She is continually shown to be caring, although it is often to her detriment. Such as putting up with her brother tempers and saving the Lhazar women. She is also very loyal to her husband forming a close bond with him and even sacrificing herself on his funeral pyre.