She's the beautiful golden haired girl summoned by Shiro to the grail war as Saber. While she is said to be the most powerful servant, she is stuck with someone who isn't much of a magus. As Saber became better acquainted with Shiro, she realized that he's a good person aligned with her own ideals. Saber's amazing combat skills are innate because she has wholly embraced the way of the warrior. This leads to her very logical way of thinking, and tranquil presence.
Her personality varies across the different stories. In Fate, Saber is almost completely stoic. No matter how much Shiro tries to thaw her cold attitude, she's disciplined and distant. In the other two stories Saber is a bit more friendly and feisty. While she claims to be indifferent, Saber enjoys Shiro's cooking and eating in general. She conspicuously comes up with reasons they should eat if it ever looks like they'll potentially miss a meal. Saber may be nearly impossible to read by outward appearances, but she reveals a lot about her mood and what she's thinking by the way she eats.
Saber is exceptional in combat. Few, if any servants; can match her in melee. She also has extreme magic resistance. One of her abilities is to quickly gage combat skills, strengths and weaknesses. This allows her to quickly invent counters to nearly every kind of attack. Her main noble phantasm is Excalibur - which is basically a big sword hit but with enough force to cause dramatic explosions.
Saber's true name is Arthuria: the heroic legend that king Arthur is based off of. After pulling the sword from the stone she became king, but had to hide she was a girl. From that time forward she thought of herself as no longer human, but simply as a king. Every action and decision was only for her kingdom. Each battle was fought to minimize losses, however these were often not compassionate choices. As time passed, people around her became alienated. The harder she tried to be perfect, the more people came to detest and distance themselves from her.
This eventually led to her defeat on a lonely hill. With death in sight and the loss of her kingdom inevitable, she prayed for salvation to protect the things she had fought so hard for. Through this she was able to become a heroic spirit, however unlike most heroic spirits this happened before she died. Instead she enters the grail war in history, and afterwords returns to the point right before her death. This means she doesn't have a spirit form like other Servants, and can remember events in past grail wars.
Shiro's link to Saber allows him to see her past in his dreams. The more he learns about her story, the more angry he becames that she was never really happy in life. No matter what she did in service of her country, it was never appreciated. Shiro becomes determined to bring her happiness, but discovers that he doesn't know how to make people happy, only help them. Much like Saber.
If you have no chance of victory, I shall make one for you.