Abishag was King David's attendant in his elderly years. Coming from the the city of Shunem in Issachar, Abishag was considered one of the most beautiful women all of Israel. As David's attendant, Abishag's chief duty was to lie in bed with the elderly David to keep warm at night (known as gerocomy) and it was very likely it was intended for her to have sexual relations with him (which did not occur). After David's death, his firstborn son, Adonijah tried to usurp the throne from Solomon by asking for Abishag's hand in marriage. Other than her minor role in the court affairs of David's family, Abishag has no other appearances or description in the Bible; she simply appears a stock character as part of the whims of the males of her time.
Abishag was a Hebrew woman born in the Tribe of Issachar. She lived in the village of Shunem during her early life. She was named "Ignorant Father", perhaps reflecting that she had a foolish father. As a young woman, she became exceedingly beautiful, but was not married before being conscripted into royal service.
When David became elderly, he had poor circulation and was unable to keep warm in bed. Very possibly, David was experiencing impotence. Seeing David was unable to stay warm at night and losing the virility of his youth, David's staff wanted to preserve his health and youth, thus continuing his prestige as king. His servants suggested that a national search be made for a beautiful young virgin who could care for the king in his old age: namely to lie with him at night to keep him warm and very possibly to have intercourse with him and help him remain virile. 
While Abishag lied in bed with David at night, he never had sexual relations with her. During the daytime, Abishag served David and met his needs. She was David's primary caregiver, with David's wives tending to their own affairs much of this day. This is evidenced by when Bathsheba went to speak to David in his chambers, Abishag was attending him.
A short time later David died and Solomon became King. With her master dead, Abishag was now a servant of King Solomon. Solomon's brother and David's eldest son, Adonijah, noticed Abishag's beauty and wished to have her as a wife. Adonijah wanted the throne and having Abishag as his wife would also take power from his brother. Adonijah came to Bathsheba and asked to her to ask Solomon to give Abishag's hand in marriage to him. Adonijah reasoned that the Kingdom was his, but God's decree forfeited his right to King. Having Abishag as a wife would be pleasing to him and a method for him to gain power he felt he deserved.
Bathsheba went before Solomon and asked him to give Abishag's hand in marriage to Solomon. Hearing this Solomon was outraged, suspecting that Adonijah wished to usurp the throne from him. Adonijah was executed and some of his associates were also killed or exiled.