Parallel worlds, also known as alternate realities, alternate timelines, and branching timelines, are self-contained, separate realities coexisting alongside one's own that exist as historical variants of one base universe (natives of a particular reality always consider their own world to be the "base", regardless of which reality they inhabit). This differs from Alternate Dimensions, which are separate realities that coexist with the base universe but that do not necessarily have any sort of variational relationship with the base universe at all. A universe identical to this one but in which John F. Kennedy was never assassinated would be a Parallel World; a universe where all of reality is a fiery pit ruled over by demons would be an Alternate Dimension.
The existence of the supervillain called Moebius, as well as the presence of certain other individuals on Earth, has proven to most theoretical physicists that parallel worlds exist. These alternate timelines are usually very similar to "Standard Earth", but have differences when it comes to the historical record. A study done by scientists at Oxford University, with the assistance of a twenty-two year old metahuman who called himself "Pockets" revealed that the Many-Worlds Interpretation (MWI; the theory that all observable quantum events occur simultaneously in all ways possible, with reality splitting off into a new Parallel World for every possible outcome) is true.
This means that, theoretically, billions of new universes are "born" every day. Consider: a person wakes up in the morning and walks into his kitchen to have breakfast. When he makes a decision about what to eat, the universe splits into Parallel Worlds. In one Parallel World, he has cereal with milk. In another, he has toast and coffee. In a third, he has oatmeal. And so on and so on to the extent of his possible choices for breakfast (including a world in which he skips breakfast entirely. These worlds are further split by associated decisions: what brand cereal does he eat? Does he add fruit to his cereal? And if so, what kind of fruit? Does he accompany his cereal with some sort of beverage? If so, does he drink milk, or coffee, or fruit juice? And if he drinks fruit juice, what type of juice is he drinking? And then after breakfast, he goes to get dressed for the day and the universe again splits when he decides what to wear.
What was discovered, however, is that most of the time these "minor alternatives" tend to remold seamlessly with their origin reality with no one ever the wiser. It is only when the event is one of "landmark proportions" (to use the phrasing of Dr. Sylvia Dyner, head of research on the project) that the realities stay separated and continue with their historical flow.
Researchers have discovered the existence of Earths where the Confederates won the American Civil War, where the Russian Bolshevik Revolution of 1917 is remembered as a total failure, where the Third Reich still rules over much of Europe, and where various public figures were assassinated (or not as the case may be) who are still alive in the base world.