The name "Silmarillion" can mean the published book (as in The Silmarillion), but it can also mean all the stories from the First Age of Middle-earth (the Quenta Silmarillion).
Overview
The published The Silmarillion has five parts:
The Ainulindalë tells how Eru Ilúvatar (God) created the Ainur and the universe (called Eä). It talks about a character named Melkor who is jealous of Eru Ilúvatar’s power and wants to sing differently from the rest of the Ainur.
The Valaquenta tells of the Ainur who came into the world, where they were known as Valar and Maiar. Melkor starts destroying everything the other Valar make. If they make a valley, he raises it up again.
The Quenta Silmarillion tells the stories of the First Age of Middle-earth. It is about the wars of the Elves and Men against the Dark Lord Morgoth, and the fight for the Silmaril jewels. The Quenta Silmarillion is the biggest part of the book.