What does it mean to create a new world in Dwarf Fortress? Is a world the same as a game?
The world is where you create new games, you can play many games in a single world.
You may want to create a new world if you are toying with world creation parameters:
By altering these parameters, you could generate a world made only of ice and magma, where you are under constant siege by Goblin hordes. If you're finding the game too easy on standard settings...
A world is the environment around your fortress/adventure, all the actions you do have influence on this world, and you can play several fortress after each other inside the same world.
However, there are certain limits on this, such as there can only be one active fortress in each world, requiring you, if you want to play another fortress without abandoning your current one, to create a new world.
Each world you create can have a single game being played in it at a time.
You create a world (named "Shards of Beer" or something). You make an adventurer, and adventure for a while. You retire that adventurer and start a fort (which will be founded in the same year you stopped adventuring). If you abandon that fort, you can then reclaim it with another expedition, or start a new fort somewhere else, or start another adventurer (and maybe go find your old fort...)
While all that is going on, you can create a separate world "SheepDeath". This world is completely separate from the other one--none of the forts from the Shards of Beer will appear in this world, nor will any of your adventurers be in the legends of this world.