Simply put, it provides efficient data retrieval.
Taking the phone book, it is always a "last name, first name" so you can find someone. Imagine if the telephone company simply added new numbers to the end of the list without any orders: you would have to scan millions of records one by one to find Smith, John.
Well, the same goes for the database table. A table without an index is (simply) called a "heap": because your data is literally a bunch of unordered data. If I have a million lines, I have to look at each line to find what I want.
Of course, this is more complicated than that, but I hope this reflects the essence.
The same applies everywhere: street names in the AZ manual are always in alphabetical order, the entries in your bank statement are always listed in date order
gbn
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