Quest

From Diablo Wiki

A Quest is some kind of a question that an NPC has for you. The NPC will have an ! above his head, or he/she greets you, while you were not clicking on him/her. Clicking on the NPC will open a frame in which you can see what he wants from you. He also will tell you where you have to go, although he wouldn't tell you the exact place. You can read the quest text back by pressing on Q.

If you have done as the NPC asked you, you will get a reward. That can be one or two Skill Points, five extra Stat Points, an item. The last quest of an Act often grants you access to the next Act, or next Difficulty.