As a child, Shiro was nearly killed in the devastation of the fourth grail war. Close to death he's rescued by Kiritsugu and later adopted by him. Visions of the disaster continue to haunt Shiro, and his rescue lays the foundation for his desire to become a hero who can help and save people. The night before Kiritsugu dies, he tells Shiro that he can no longer become a hero, so Shiro vows to become one in his place.
Shiro has long studied magic, but as Kiritsugu refused to teach him much, Shiro struggles with even the basics. He's become good at analyzing things, and can strengthen them to some extent. Every night, Shiro spends time trying to train by strengthening objects, but often with poor results and little improvement. Later Shiro finds he can also create copies of certain types of objects.
One major aspect of Fate Stay Night is Shiro's quest to become a hero. In Japanese this is Seigi no Mikata - Hero of Justice, but there isn't an exact equivalent translation. Becoming a hero is his ideal, but the underlying theme is the sacrifice and conviction necessary to become one. In each of the three stories Shiro has to come to grips with his ideal in different ways, and the results aren't always the same.
Shiro's defining feature is his force of will. He simply does not give up. No matter what the odds, no matter how much effort it takes, even if it seems impossible; Shiro will keep trying and will give it his best effort. As a hero, his persistence is a virtue, but in daily affairs he's known for being stubborn.
If you walk down the path that you believe is right,
you cannot be wrong.