Claire meets Jamie when he's injured, which is fitting since getting hurt happens a fair amount in the time period Jamie lives in; axe wounds and musket shots aren't all that uncommon in Jamie's line of business (being a warrior) in the 18th century. He's not just a tough guy, though, and he wins Claire's heart, even though their marriage happens more out of necessity than romance. To this end, his soft side and his bravery come together when he risks his life to save Claire on multiple occasions, even almost dying in the end.
As a general rule, nobody breaks Jamie's stride, and despite being wounded on several occasions, Jamie pretty much brushes himself off and gets right back in the game (or on the battlefield, as the case may be). However, Jamie almost crumples completely after being raped by the cruel British commander Jonathan Wolverton Randall, a rape he chose in order to save Claire from Randall's wrath. With the love of his wife, though, he's ultimately able to get through this traumatic ordeal, recovering in France, away from the violent battlefields of the Scottish Highlands.
When he isn't offering himself in Claire's place, Jamie's main motivation throughout most of the book is to clear his name. He was framed for a crime he didn't commit (although he's getting away with a lot of crimes he did commit). Unfortunately, though, the man who actually did commit this crime (shooting an officer) is none other than Jonathan Randall, Jamie's arch-nemesis, rapist, and an all around terrible dude.
In short, Jamie is handsome, a bit of a bad boy, but still a true gentleman. In other words, he's your classic romance novel hero: a warrior who is sensitive at heart and hot in the sack. Just check out Diana Gabaldon's Facebook page on any given day to see how many readers get all hot and bothered by Jamie Fraser.
One reason for this outpouring of adoration is that we get to fall in love with Jamie right alongside Claire. Their early relationship consists of him getting injured, Claire treating him, and then Claire getting mad at him for not resting. She's very motherly to him, just wanting to take care of him, and eventually this translates into the bedroom as well as the operating table. Hey, what can we say? Claire is good with her hands. Plus, in a sea of danger and uncertainty, Jamie proves himself to her time and again; he's as steadfast a hero as they come.
Jamie is kind of like a male version of Merida from Brave: headstrong, fiery hair, good with weapons, probably able to wrestle a bear with his bare hands. Aside from that, we don't learn too much more about this gallant Scottish man.
He has a strong moral code, which we see in his desire to protect his sister, his wife, and, well, any other woman whom he feels is being treated wrongly. He even takes Laoghaire's punishment early on in the story, even though he doesn't really feel anything romantic for the girl. As a result of his pride, he has a web of scars across his back. Dougal Mackenzie exploits these scars (inflicted at the hands of Jonathan Randall) to rouse sympathy for the Jacobite cause, though Jamie does not like being used.
Jamie is also conflicted about the death of his father. His dad died watching Jamie being whipped in prison, a whipping Jamie decided to take instead of submitting himself to Jonathan Randall's sexual urges. A lot of Jamie's actions near the end of the book stem from this kind of guilt—for instance, he ends up submitting to Randall because he's afraid someone else, namely Claire, will die if he doesn't. Plus, he feels guilty about failing to protect Claire from a previous incident in which they were attacked near a river.
So let's recap: Sexy, strong, Scottish accent, strong moral code—no wonder everyone is in love this man. When Jamie tells Claire "I am not 'many men'" (15.69), we don't doubt him for a moment.
And maybe we fan ourselves a little bit, too.