The Surgeon's Mate is one of the cleverer titles for an Aubrey/Maturin novel, suggesting that it does that Dr. Maturin is at last going to get some help in keeping Captain Aubrey's crew healthy; larger commands like those Aubrey is entitled to these days not only get to bring along a surgeon but also a surgeon's mate, but that's not even sort of what is going on here.
The title refers to Maturin's lady-love, Diana Villiers, who has at last agreed to marry him as a means to recover her British citizenship after having run away with a rich American several novels ago -- a move she came to regret by the time The Fortune of War brought Aubrey and Maturin to America. Partly with her help, our duo escaped from the clutches of her lover (who turned out to be a major American spy-master) after having killed some important French spies, and made off with some of the lover's very important personal papers to boot.
It's a strange courtship these two have had, and by the time Maturin has found Villiers again, in America, he's mostly out of love with her; she has taken up tobacco smoking and bourbon drinking and a bit of a colonial accent, but she's still a looker and a pretty cool chick, so he's not completely off her, and good thing, because in The Surgeon's Mate it's her turn to save his bacon. Well, sort of. She believes she has done so, and is going to be allowed to believe it, because if the real story of how Stephen escapes France (where he and Aubrey are taken prisoner after their sloop wrecks after assisting in a chase after a mission in the Baltic involving Catalan freedom fighters and a Swedish island battery and other complicated stuff) ever became common knowledge, he would no longer be able to deny being the George Smiley of the Napoleonic wars.
This is not my favorite Aubrey/Maturin by a long shot, choppy and sort of all over the place, but it's still good fun.