Accuracy, also referred as Acc or Offense, determines the chance your ship's cannons hit the enemy ship (or fort if that matters).
Accuracy is a number, in %. At maximum range (default 750 yards), your accuracy is only ~13% with Round Shots, but can even drop to ~10% with Bar Shot. At minimum range (if your target is like 50 yards away) your accuracy will always be 100%.
[Basic 1]: Accuracy is dependant on your distance (range) to your target, but also gets influenced by the Cannon Ammunition you use.
However, at mid range (in the middle of min. and max. range), default 375 yards, accuracy will not always be 50%. This is because some Cannon ammunition is limited in range, for example, Bar Shot is limited at 90% max. range (default 675 yards) or Star Shot is even limited to 50% range (default 375 yards)! It's obvious that ammunitions with limited max. range, gradually suffer more accuracy loss at range. Therefore, in this example, if you want to Demast your target at 375 yards, it's better to use Bar Shot instead of Star Shot. The additional Damage gained from Star Shot (compared to Bar Shot) doesn't do it's job, because your accuracy will be too low. Luckily there is also Chain Shot, which is better at mid. range than Star Shot, but worse at short range. It also losses to Bar Shot on long-range.
[Basic 2]: Learn the advantages and disadvantages of every Cannon ammunition!
Accuracy gets influenced by a lot more factors than the two (2) mentioned above.
[Basic 3]: Accuracy is also dependant on your and your target's ship speed.
This one is also obvious. Imagine you are racing in a car and trying to shoot paintball bullets on your mates, who are also racing in a car. This is a lot more difficult than shooting at each other with just walking/running, heh? It works the same in PotBS, the higher your and your target's ship speed are, the more difficult it is to hit. Especially if you are sailing away from each other!
[Basic 4]: Target Tracking reduces the loss of [Basic 3].
Target Tracking (TT) reduces the accuracy penalty you get when you or your target is moving. It works a bit complicated so let's try to say it simple. For every one (1) knot of speed, you need one (1) Target Tracking. A ship receives a 2% penalty to accuracy for each knot of speed. The Target Tracking of the ship reduces this penalty by 1% for each point. Using Battle Sails (B) is a great way to make sure your cannons hit! Ideally, your accuracy is highest if you and your target aren't moving.
*Do note that Accuracy is subject to Stacking Penalties.
In the end, if you want to deal Damage, close the distance (range) between you and your target. If you want to avoid damage, keep at long-range or (even better) stay out of range of your enemies cannons (750 yards+).
This information is provided by the update that PotBS Wikia is undergoing, by Captain Vuur.