The main attraction for most fans of Dwarf Fortress is Fortress Mode, where you manage seven dwarves of varying skills. These dwarves will construct a fortress based on your chosen biome and starting equipment. Afterwards, you need to keep them happy with food and alcohol. Your dwarves can take on different jobs within the fortress, such as mining, woodcutting, masonry, and jewelry.
The goal is to survive for as long as possible, but at some point your game ends when all of your dwarves die from a hostile encounter, illness, or old age. With the lessons learned from your latest group of dwarves, you can start the game anew and attempt to keep your dwarven population alive for as long as possible.
If you want a change of pace, try Adventurer Mode, which allows you to create a single character and travel the game world to take on quests and fight enemies.