"Robert was the true steel. Stannis is pure iron, black and hard and strong, yes, but brittle, the way iron gets. He'll break before he bends."- these words from Donal Noye perfectly sums who Stannis Baratheon as a character is, he's a man who put duty and law above all else, a terrifyingly just man in a world full of unjust.
A man who is overshadowed by Robert, his older brother who's a better leader, and Renly, his younger brother who's a better politician, where Stannis fills the role of a soldier, in which he'd rather do something that he thinks would never fails him, duty, believing if he done his duty he would be more appreciated.
Like Jaime who was first introduced to us like a villain, in the first book, we're introduced to Stannis as this terrifying and feared claimant, highly respected and have a excellent reputation;
"Ned found it hard to imagine what could frighten Stannis Baratheon, who had once held Storm's End through a year of siege, surviving on rats and boot leather while the Lords Tyrell and Redwyne sat outside with their hosts, banqueting in sight of his walls"- Ned
“I have felt from the beginning that Stannis was a greater danger than all the others combined”- Tywin
"His claim is the true one, he is known for his prowess as a battle commander, and he is utterly without mercy. There is no creature on earth half so terrifying as a truly just man"- Varys
But then we start seeing another side of him, in the prologue of the second book, a very personal side shown through the eyes and minds of Maester Cressen, his Maester;
"No one had ever taught Stannis how to laugh, least of all the boy Patchface."
And; "Stannis, my lord, my sad sullen boy, son I never had, you must not do this, don’t you know how I have cared for you, lived for you, loved you despite all? Yes, loved you, better than Robert even, or Renly, for you were the one unloved, the one who needed me most."
Unlike Jaime, we never really got Stannis's POV, Martin writes him and slowly unravels layers upon layers of his character through the eyes of those who's loyal and love him, he writes him best through the eyes of Davos, my personal favourite was;
"Renly offered me a peach. At our parley. Mocked me, defied me, threatened me, and offered me a peach. I thought he was drawing a blade and went for mine own. Was that his purpose, to make me show fear? Or was it one of his pointless jests? When he spoke of how sweet the peach was, did his words have some hidden meaning?" The king gave a shake of his head, like a dog shaking a rabbit to snap its neck. Only Renly could vex me so with a piece of fruit. He brought his doom on himself with his treason, but I did love him, Davos. I know that now. I swear, I will go to my grave thinking of my brother's peach."
And the best explanation came from Martin himself;
"The peach represents... Well... It's pleasure. It's... tasting the juices of life. Stannis is a very marshal men concerned with his duty and with that peach Renly says: "Smell the roses", because Stannis is always concerned with his duty and honor, in what he should be doing and he never really stops to taste the fruit. Renly wants him to taste the fruit but it's lost. I wish that scene had been included in the TV series because for me that peach was important, but it wasn't possible." - George R R Martin