Why do some physicists think parallel worlds might exist?

I have read in a book on quantum mechanics that some physicists believe that parallel worlds might exist. However, what I understood from the book is that if you assume many worlds actually exist, Schrodinger cat problem can be solved. And I could not understand the logic behind it. What was the conclusion... show more I have read in a book on quantum mechanics that some physicists believe that parallel worlds might exist.
However, what I understood from the book is that if you assume many worlds actually exist, Schrodinger cat problem can be solved.

And I could not understand the logic behind it. What was the conclusion given by what experimental result? And how does "many worlds interpretation" solve what problem?

Could anyone please give me step-by-step explanation, hopefully with words, not with many mathematical expressions.
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