Meet Captain Jack Aubrey. A burly, bluff sort of cove, not perhaps the sort of man you'd sit down with for a nuanced discussion about politics or the binomial theorem, but a natural leader of men and an experienced naval commander. His skills are less well suited to land-based matters, and as the result of some unwise financial investments he finds himself in a state of mild disgrace as the novel opens, and jumps at the chance to take command of HMS Worcester for a mission to bolster the British blockade of Toulon. This is a tedious mission involving a lot of waiting around, and on a ship that is well-known to be badly-built, but Jack decides that it's still better than being beset by lawyers and creditors on land.
Meet Stephen Maturin. A doctor, Irish-Catalan by birth, and Jack Aubrey's closest friend and advisor and regular ship's doctor. Maturin is a shrewd and secretive character, as befits someone who does a bit of clandestine naval intelligence work on the side, so he and Aubrey are like chalk and cheese, but, hey, opposites attract. Maturin signs on to fulfil his usual ship's doctor role on the Worcester, the two say goodbye to their wives and off they go.
As expected the job they've been asked to do is exceptionally dull, basically involving sitting in one place in a line of ships and making sure no French vessels try to make a run for it. A bit of excitement is provided by a brief mission to a supposedly neutral port in Tunisia to try and provoke the French ships stationed there into firing first and starting a fight, but they basically just shrug Gallicly and refuse to be tempted, leaving Jack frustrated.
His mood is not improved by having to do some sneaky night-time duties to facilitate some of Stephen's spying activities, dropping him off via dinghy on a deserted bit of marshland (somewhere in the vicinity of the Camargue, we're invited to assume) and picking him up later after a botched mission, with his British contact in tow with an accidental self-inflicted gunshot wound. Back at the blockade, things seem to be looking up when some of the French ships make a dash for it, and the British set off in hot pursuit, but the wind changes at a crucial moment and the French are able to return to port without any serious damage.
Having bent Worcester all out of shape in the furious pursuit, Jack takes her to Malta for repairs and is assigned his old frigate HMS Surprise for a delicate mission to the Ionian Sea (the triangular bit between western Greece and the bootheel of Italy, basically) - the idea being to play off some of the local beys against each other to Britain's advantage and retake some of the key islands (including Corfu) from the French. Having chosen the best strategic ally, Jack then finds himself becalmed in harbour (in what would be modern-day Albania) before escaping and launching a furious pursuit of one of the rival beys who wants to scupper Britain's interests. Meeting him at sea (and with Surprise outnumbered by two ships to one) a furious naval battle ensues with much indiscriminate dispatching of grapeshot and cannonballs flying around taking people's limbs off. Jack gets to work off some of his frustration at being denied a proper battle earlier by doing some proper boarding and cutlass-wielding activity, a surrender is obtained and Jack and his crew live to dress their wounds, claim some booty and head off for further adventures. Hurrah!
One of the things about picking books up randomly second-hand is that you often get hold of one that turns out to be part of a series, and the law of averages dictates that it'll seldom be the first book. So you then have to decide whether this is a self-contained story that just features some recurring characters (The Redeemer is a good example of this), whether you really need to read the series in order for it to make any sense (the Girl With The Dragon Tattoo series, for instance), or something in between: linked stories, recurring characters, probably better to read the whole thing in the right order but you can read individual ones and they'll still make sense (the Ripley novels, say).
The Ionian Mission probably falls into the last category (what posh literary types call a roman-fleuve): it's the eighth book in what's generally known as the Aubrey-Maturin series, which comprises twenty books (there won't be any more as O'Brian died in 2000). So while it's probably better to have read them in order in order to pick up on some of the references to previous adventures and to better understand how some of the minor characters fit into the overall context, it's certainly not essential.
The novels were published over the course of thirty years (1969-1999; The Ionian Mission was published in 1981) and describe events over a period of roughly fifteen years between 1800 and 1815. Their critical reputation has taken a gradual upward curve over the years, from being regarded as a sort of modern-day Hornblower saga to being the work of (as the blurb on the front of my copy says) "the greatest historical novelist of all time". I dunno about that, but I enjoyed it very much - the evocation of life on board ship is exceptionally vivid, even though O'Brian makes no concession to those who aren't familiar with sailing and naval terminology. The structure of the novel would be slightly odd if it were not understood that this is part of a long series - the "Ionian mission" of the title only materialises around page 250 of a 350-page book, and the battle with the Turks at the end occupies only the last 15 pages of the book. Stephen Maturin's brief spying mission is ill-explained and seemingly inconsequential as well, though I'm sure it fits in as part of a longer narrative.
More generally, certain conclusions about the series and characters can be drawn from this single instalment, most obviously that Maturin is a sort of authorial alter ego, with Aubrey perhaps representing some personality traits that O'Brian wistfully aspired to. Maturin also acts as a sort of Basil Exposition for various bits of arcane naval stuff, generally via the vehicle of having some lubberly hanger-on saying "I say, Dr. Maturin, what does the captain mean by "luffing"?".
So while I'm not sure that naval adventure fiction, however subtly and intelligently written, is ever really going to be My Thing, and I'm not going to be rushing out to stock up with the other 19 books in the series, I wouldn't rule out reading another one or two in the future.
Many people will know the novels through the film adaptation Master And Commander: The Far Side Of The World, which came out in 2003. The horribly-botched title reflects the idea that this was intended to be the first of a series of films, a series that in the end never materialised (although the first film was a modest commercial success), though there are still those who'd like to revive the idea. But it did at least perform the almost-impossible task of getting both the Hitchens brothers to agree about something - basically that the film was fine, but the books are better.