There are two assumptions underlying the many-worlds view. The first is that the wavefunction is not simply a description of the object's state, but that it actually is the object. The second is that observation has no special role, unlike the Copenhagen interpretation which considers the wavefunction to collapse upon observation. Under the many-worlds interpretation, the Schrödinger wave equation holds all the time everywhere.
Various consequences follow from these assumptions. An observation or measurement of an object by an observer is modelled by applying the Schrödinger wave equation to the entire system comprising the observer and the object. One consequence is that every observation causes the universal wavefunction to decohere into two or more non-interacting branches, or "worlds". Since many observation-like events are constantly happening, there are an enormous number of simultaneously existing worlds.
If a system is comprised of two or more subsystems, the system's state will typically be a superposition of products of the subsystems' states. Once the subsystems interact, their states are no longer independent. Each product of subsystem states in the overall superposition evolves over time independently of other products. The subsystems have become entangled and it is no longer possible to consider them independent of one another. Everett's term for this entanglement of subsystem states was a relative state, since each subsystem must now be considered relative to the other subsystems with which it has interacted.
Mathematically and physically, the many-worlds interpretation is simpler than the more widely accepted Copenhagen interpretation. The act of observation or measurement is not magical, and the interpretation of probabilities as the squared amplitude of the wave function is a direct consequence of the theory rather than a necessary axiom.
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