The World
Geography
One Piece takes place in a fictional world where most of the planet is covered in water. Only one continent, the Red Line, exists and it runs continuously north to south along the center of the globe. Running opposite to the Red Line is the Grand Line, a massive ocean current that circles the globe east to west. Together, the Red Line and Grand Line divide the waters of the world into four separate oceans: North Blue, East Blue, South Blue and West Blue. Most of the people in the world live in these four quadrants.
The Grand Line is known as the pirate's graveyard; it's a dangerous place that's cordoned off from the rest of the world by two windless barriers known as Calm Belts. These Calm Belts have no currents at all so most ships who cross into these areas usually find themselves marooned. The Calm Belts are also dangerous for another reason: they are the home of thousands of sea kings -- massive and ferocious monsters who can easily take out even the largest of ships.
The Grand Line itself is composed of several chains of islands and if one wishes to navigate through these chains, they need to use a special compass known as a Log Pose. As each island in the Grand Line is composed of special minerals that create unique magnetic waves, a normal compass wouldn't work. A Log Pose will take some time to adjust to the user's current island and then its needle will begin to point to the next island in the chain, allowing a navigator to find their way through the Grand Line. In the second half of the Grand Line, the New World, sailors must make use of special Log Poses with three needles because the islands there sometimes change their magnetic fields or hide them altogether at random. The needle that seems the most stable out of the three will provide the safest past to navigate through. It's an ironclad rule that a Log Pose never lies.
The islands along the Grand Line all have unique climates that are classified into Spring, Summer, Fall or Winter and each of those have their own four seasons. This is another feature that makes navigating the Grand Line a challenge because the weather can change dramatically in a single voyage, something that doesn't happen in anywhere else. One can tell they are nearing a certain type of island once the climate begins to stabilize.
Races
While humans are the dominate species in the world, there are many other races that also populate the planet. Fishfolk and merfolk are the most well known but were unfortunately classified as fish by humans until about 200 years ago. Much of the racism and prejudice that humans had against fishfolk and merfolk still exists today and as a result, fishfolk and merfolk tend to hate and distrust humans.Fishfolk and merfolk differ from each other in that merfolk are your typical mermaids of legend; they have human appearances on their top halves and fishtails on their bottom halves. Fishfolk have humanoid bodies with webbed hands/feet and sport characteristics of specific fish (ie: octopus fishmen may have multiple arms with suckers). In the series, characters usually refer to merfolk as "mermaids" and fishfolk as "fishmen" but both genders exist in both species.
Another somewhat common race along the Grand Line are the giants. In One Piece, the first giants we meet are from the great warrior country Elbaf but there are many other giant countries in the world and some of them are even peaceful! Giants are exactly what you imagine them to be: incredibly tall humanoids who are all vastly powerful.
There are many other kinds of races in One Piece but I feel that talking about them would ruin the surprise of learning about them for the first time while reading the series!
Devil Fruits
Strange fruits exist in the world that, when eaten, grant the user unique powers. The caveat is that they are no longer able to swim and lose all their strength when submerged in seawater. These fruits are known as devil fruits.
Only one of each devil fruit power exists in the world and once it has been eaten, the devil fruit will only reappear as a fruit in the world once the user has passed away. Since these fruits are recycled through death, there exists a book that lists the fruits along with their names, illustrations and descriptions of their powers. There's still a lot of undiscovered fruits that aren't in this book but it exists as a means for people to know which devil fruit grants what power simply by looking at it. As legends go, it's one devil fruit power per person, so being able to know what you're going to get before you eat it is rather convenient!
Devil fruits can be classified into three different types: logia, paramecia and zoan. Logia fruits are the rarest and most powerful as they allow the user control over a specific element and allow the user to turn their body into said element itself. Paramecia fruits are the most common and allow the user to alter their physical bodies in some form or allows them to manipulate substances, people or the environments around them. Zoan fruits allow the user to transform fully into an animal or half-human, half-beast form.
Government
About 800 years ago, twenty individual kingdoms across the world came together to form the World Government. Nineteen of these rulers settled in the holy city of Mariejois, leaving their kingdoms behind and eventually becoming the World Nobles (aka Tenryuubito). Due to their relation to the World Government, the Tenryuubito exist outside of its realm of influence and are able to do whatever they please, from owning slaves to committing murder in broad daylight. Currently, about 170 different nations are part of the World Government and every four years, the leaders of these nations gather at what is known as the Reverie, a grand summit to discuss world politics.The World Government itself is governed by the Gorosei, give mysterious elders that control all branches of the government: the Marines, Cipher Pol, the Shichibukai, Impel Down and any other related organization. They are not, however, above the authority of the Tenryuubito. There is much corruption within the World Government and as a result, it often acts as the antagonist to the Straw Hats. There is hope for it, however, as there are many Marines who wish to see true justice being delivered to the people of the world.