Many of Freud's contributions to psychology were revolutionary for their time, despite the modern view that he was mostly incorrect. His most important concept was that of the importance of early childhood on the development of the mind and personality. He revealed that the events in a child's life between the ages of 0-1.5 (the oral stage), 1.5-3 (the anal stage), and 3-5 (the phallic stage) affect the development of the child's personality in different ways. Prior to Freud's theories, the Victorian concept of children was that they were simply smaller adults, and were treated as such (without regard to the child's psychological state).
Freud put a large amount of emphasis on sexual instincts, to the chagrin of his peers and followers. He theorized that sexual desires were the base of each stage, and the base of a different conflict at each stage. A fixation in that stage would be caused by improper treatment of the child (an unresolved or misresolved conflict due to lack of or excessive gratification).
The oral stage is characterized by placing objects into one's mouth (as long as they fit). According to Freud, biting and sucking things gives sexual pleasure as well as nourishment. The conflict here is of course the amount of oral gratification in the form of breast feeding. Fixation in the oral stage could lead to dependency, gullibility, or excessive optimism or pessimism.
The anal stage is characterized by releasing waste through the anus. Generally, this stage is the time when children are "potty trained". Sexual gratification is given through contraction and release of the anal muscles during the release of waste (control of these muscles does not become voluntary until this stage). The conflict is with the parents, and has to do with potty training: the child resists potty training, opting for gratification instead of self-control. Fixation in the form of anal-retentiveness is caused by harsh potty training, and results in perfectionism, a strong need for order, or cleanliness. Fixation in the form of anal-expulsiveness is caused by too much gratification, and results in carelessness, messiness, or even sadism.
The phallic stage is characterized by stimulation of the "phallic region" - the penis or clitoris. Sexual gratification is caused mainly through this erogenous zone, and conflict arises when parents discipline the masturbation of the child. Due to this conflict, the child becomes attached to his or her parent of the opposite sex, but generally resolves this conflict by the age of five or six. Fixation in this stage (by not resolving that conflict) could result in (according to Freud) oral or anal stimulation, masturbation, and sexual activity with people of the same gender, which Freud viewed as "pregenital fixations inconsistent with the life instinct, eros". Resolution of this conflict leads to a latency stage, in which no sexual gratification is desired, and finally a genital stage at puberty, the "normal" sexual stage in which people are attracted to those of the opposite gender, but not their parents.
While Freud may have missed the mark on the specifics (modern research has shown that his views on the "fixations" in different stages were incorrect), his attention to early childhood was important given his time period. Previous to Freud, people commonly ignored the development of children and attempted to treat them as they would treat adults (as was normal in the Victorian era), leading to all kinds of psychological problems. Freud even influenced the artistic and literary movement of Modernism as an escape from the constraints of Victorian society.