Completing missions advances your character's development and progresses your story.
The triangle icon over a character's head means that he or she has a mission available for you. Right-click on the character to start a conversation and learn more about the mission.
Some missions may require content access to be purchased before accepting the mission; these triangle icons will display the Cartel Coin symbol.
The same icon on your minimap marks the location of a character with an available mission.
Accepted missions appear in the mission tracker in the upper-right corner of the screen. The light-blue text tells you what to do next in the mission.