She's malicious and seemingly evil, but also has an easy going and quirky personality. Magic may seem like a great skill, but is easily countered by most heroic spirits (who have abilities of legendary proportions). Caster's trump card isn't her magical abilities, it's her superior intelligence and scheming mind. Caster's story isn't seen from the beginning, but after her betrayal of the first magus who summoned her. Without a link of a magus, caster nearly passed from the world but was found by Kuzuki Soichiro. While an unlikely ally, he forms a contract with her anyway. He never asks anything of her, and obediently follows her plans. Even when told of the hard to swallow story of the grail war; when asked if he believed her, he only trustingly asks if she was lying.
Caster finds Kuzuki to be much at odds with any man she's ever encountered. During her life she had been used as a tool or pawn, now as a servert she is only summoned in the grail war to again be used as a means to an end. Yet this man asks nothing of her, and expects nothing. He simply does as he is told. Caster would make any regular man her minion, yet this is totally unnecessary for Kuzuki. In this way she comes to treasure him, and views his detached personality as an endearing feature. Caster likely originally sought the grail to further take vengeance on humanity that had caused her pain in life, but after meeting Kuzuki she seeks it to live a second life with him.
Caster doesn't have any particular special ability since they're all special. She was born in a magical age, the likes of which few in the present can imagine. As such, her power far exceeds that of any normal magus. Spells that could take minutes to conjure for a human, happen instantly at her fingertips. This is one reason why her partnership with Kuzuki is deadly since his martial arts abilities enhanced by her magic allow him to fight servants in her stead, and she is more than a match for any master/magus. Defensively she's adept at not getting killed by teleporting as needed.
Her noble phantasm is a simple looking dagger, however it's one of the most dangerous weapons in the grail war as it dissolves the contract between master and servant. Details on functionality are vague, but it does appear to be just an ordinary dagger aside from its special function. Against servants with supreme melee ability you'd think any attempt to use it would be easily deflected, yet caster somehow manages to connect more than a few times. It also seems as though once the contract is dissolved that this allows her to exert power over the servant. As the master is the lifeline, having that connection cut makes the servant dramatically drop in power and ability.
In her past life Caster was Medea, the daughter of a king in ancient Greece, and many tragedies befell her. In particular Medea was often betrayed, and she likewise betrayed others. Throughout it all, she was being used by someone for their own purposes. While having magical abilities, she didn't use them to harm others. Eventually people came to blame her for all the misfortunes that came about. She was considered a witch and despised by all, and Media came to hate people. If people wished to call her a witch, then she would become one and they would learn to fear her. Even so, her nature isn't really evil so she still has a quirky behavior when summoned as Caster.
While mentioning her past is a bit redundant, the important thing to take note of is that a servant is a tool in the grail war. This is the very thing Medea would hate most: being used. This makes her a particularly dangerous Servent to summon because the nature of the grail war would be a sure way to earn her resentment.