A duplex apartment is an apartment that's located in a duplex building — a building housing two near-identical units, with separate entrances, usually either side-by-side or one on top of the other.
Duplexes are often detached from any other apartments or may be in a small community of similar structures. It's rare to find duplex apartments that are part of a large complex like you'd find with standard apartments.
Obviously, the most significant difference between a duplex apartment and other apartments is that there's only one shared wall, either a wall between the units or the ceiling of the ground floor unit and floor of the top unit. Beyond that, the apartment types are largely similar apart from some minor differences.
For one, duplexes usually offer at least one of the units, and oftentimes both units, easy access to the outside. Other apartments may be deep inside of a larger building or up many floors. Secondly, a duplex apartment has a private entrance to the unit, where other apartments may not. Lastly, since duplex apartments have their own entrance, they usually also have a designated place to park, unlike other apartments.
There are obviously some good things and some bad things about renting a duplex apartment, like with any renting situation.
A duplex apartment looks about like what you would expect: a building split into two with each half containing a whole home. Most commonly, duplex apartments are split down the middle with two ground-floor units sharing a middle wall. However, some duplex apartments may be staked with a staircase between the two.