The dialogue takes place the day after Socrates described his ideal state. In Plato's works such a discussion occurs in the Republic. Socrates feels that his description of the ideal state wasn't sufficient for the purposes of entertainment and that "I would be glad to hear some account of it engaging in transactions with other states." (19b)
Hermocrates wishes to oblige Socrates and mentions that Critias knows just the account. (20b) Critias goes on to tell the story of Atlantis, and how Athens used to be an ideal state that went to war with Atlantis. (25a) Critias believes that he is getting ahead of himself, and mentions that Timaeus will tell part of the account from the origin of the universe to man.
Timaeus starts his account by making a distinction between the physical world, which is the world of change, and the eternal world. Since, "a description of what is changeless, fixed and clearly intelligible will be changeless and fixed," (29a) it follows that a description of what changes and is likely, will also change and be just likely. In a description of the physical world, one "should not look for anything more than a likely story." (29b)
He goes on to suggest that since nothing "becomes or changes" without cause, then the cause of the universe must be a Demiurge or God, a figure Plato refers to as the Father of the Universe. Using the eternal and perfect world of "forms" or ideals as a template, the Demiurge set about creating our world, which formerly only existed in a state of chaos. Plato describes this chaos as a lack of homogenuity or balance, in which the four elements (earth, air, fire and water) were shapeless, mixed and in constant motion. The essential act of the creator is to bring order and clarity to this chaos and disorder. The term "Demiurge" is a vilification by Gnostics who purported that the Demiurge was a fallen and ignorant god creating a flawed universe.
Timaeus goes on to state why the universe was created. God or a demiurge being good wanted there to be more good in the world. This notion is the kernel of Leibniz's optimism, and is an expression of the principle of sufficient reason, which states that nothing in the universe happens without a reason.
It is important to note that for Plato, the demiurge lacked the supernatural ability to create "ex nihilo" or out of nothing. The demiurge was able to only organize the "anake." The anake was the only other co-existent element or presence in Plato's cosmogeny. This is a major point of contrast between the Greek notion of God and the Judeo-"Christian" notion. The God of the Hebrews created "out of nothing." He was the only eternal being (taking into consideration the other two persons of the "Christian" godhead).
Plato conjectured each of these elements to be made up of a certain Platonic solid: the element of earth would be a cube, of air an octahedron, of water an icosahedron, and of fire a tetrahedron. Each of these perfect polyhedra would be in turn composed of triangles. Only certain triangular shapes would be allowed, such as the 30-60-90 and the 45-45-90 triangles. Each element could be broken down into its component triangles, which could then be put back together to form the other elements. Thus, the elements would be interconvertible, so this idea was a precursor to alchemy.