We tend to think of the Age of Sail as a time of swashbuckling pirates, lusty women, and fortunes to be made in Inca gold, but the truth is that most of the time, it was a pretty basic, scrape-to-survive lifestyle for the people who really lived it. They owned shops, traded stuff with each other, had the occasional setback, and generally woke up every morning to a day that would be substantially similar to the last. In that sense, Port Royale 3 is an accurate simulator of Age of Sail living for most people: not much happens, ever.
You're a sea captain, working (at least initially) for Spain. You can choose to play the main campaign as a trader or as an adventurer: the latter option ostensibly makes this a fire-and-brimstone, crossed-cutlasses action game, while the former is for those players who prefer microeconomic challenges. In point of fact, though, you spend most of your time in either game mode simply looking at an overhead map of the Caribbean and aimlessly sailing around. While Port Royale 3 spends a great deal of time on tutorial videos, hand-holding, and tooltips for the control system, it totally fails to give you a sense of context for what you're doing.
For example, there's a complicated popularity system for your alter ego, both with individual cities and the countries that control them, but it comes off feeling like an abstract number that goes up and down based on simple, controlled stimuli. Get your popularity high enough by trading the right goods and avoiding the wrong ones, or by doing missions, and you unlock the ability to construct buildings in a town, or hire more sailors there. If it's really low, well, not a whole lot happen. Your fluctuating popularity, like so many other aspects of Port Royale 3's gameplay, doesn't feel organically integrated to a larger ethos, but instead feels tacked on.
When you're not confused as to why you're doing what you're doing, you find yourself confused as to where you're supposed to be going. Often, combat or search-and-rescue missions have you head to a general area ("southwest of Corpus Christi," for example) to seek out a target. But this target is often himself in a moving ship, and you have a very small circle around your own vessels in which such ships are revealed on the map. This means that you spend far too long sailing in an endless loop, searching for the proverbial needle in the oceanic haystack of the Caribbean, while your money and time drain slowly away. When you do finally get into a fight, you find that combat, like just about everything else in Port Royale 3, is competently handled, but not particularly exciting. It's heavily based on statistics, like how many guns you have in your convoy and how many sailors you have per gun, and has little to do with how you prepare for and control the fight, so you feel very divorced from whatever action there may be.
If you prefer, you can avoid fighting pretty much entirely and simply focus on trading for a living instead. Here, however, Port Royale 3 stumbles in its attempts to create a realistic economic model. Buying high and selling low is the name of this particular game. You can buy a certain number of the two dozen trading good types at any port, and some ports produce certain goods and demand others. However, Port Royale 3 has a ridiculously sensitive supply-and-demand mechanic working in the background: if you start to buy up goods at a particular port, even a port that produces those goods in quantity locally, the purchase price rapidly rises until you cannot possibly sell the goods you're buying at a profit anywhere else (no one in the world of Port Royale 3 has ever heard of futures contracts, apparently).
This means that, because ports have everything in tiny supply compared to your average convoy's cargo capacity, you always find yourself buying very small amounts of goods and then searching desperately to find a port where you can offload them without bringing the sale price down to nothing as the buyer's supply increases. The upshot is that it takes forever to make any kind of serious money by trading, as no matter how big your fleet is, you can never get a decent supply of goods at a decent price. It can take hours of real time to earn mere thousands of gold pieces in a game where tens and hundreds of thousands are necessary to have any real impact.
Bottom line: trading in Port Royale 3 is a terrible, slow grind that sees you spending your time moving sliders back and forth ever so slightly so as not to affect the price too much, and getting very little reward for your precision. And since ship-to-ship fighting and treasure hunting are so hit or miss, you spend most of your time in Port Royale 3 trying to decide between being bored selling goods or being bored searching for something interesting to do. Multiplayer, though technically available, will likely serve as cold comfort, as it's all but impossible to find an opponent.
The saddest part of all this is that Port Royale 3 looks good and plays smoothly. It also, at least in theory, has a lot of facets: trading, ship-to-ship combat, ship-to-shore combat, two separate story campaigns, and multiplayer. But none of these offer anything that's much fun to do.