Standard quantum mechanics is made of two parts: a part that describes the unitary and deterministic evolution of a state vector, and a part that describes how a state vector randomly collapses when subjected to "measurement".
The many-worlds interpretation (MWI) cuts away the latter part. It uses decoherence to explain how the universe splits into many separate branches, each of which looks like it came out of a random collapse.

See also

External links

Decoherence and Ontology (David Wallace)
The Everett FAQ (Michael Clive Price)