Diablo 2 consists of several Quests per Act.
There are required Quests to continue to the next one, optional quests that can but must not be done and also useful quests that you should do to power up your character.
Each act got at least 1 quest that must be completed to proceed to the next act. These is always a boss kill quest where the player has to kill a great evil boss.
Act I: Sisters to the Slaughter: Kill Andariel
Act II: The Seven Tombs: Kill Duriel
Act III: The Guardian: Kill Mephisto
Act IV: Terror’s End: Kill Diablo
Act V: Eve of Destruction: Kill Baal (only within the Diablo II: Lord of Destruction Expansion)
Some acts got further quests that must be completed in advance before the final boss quest can be done.