What does the phrase 'much the most" mean?

Is it really a phrase? I found it in Tom Sawyer - "...and the most hospitable and much the most lavish in the matter of festivities that St Petersburg could boast..."

Solution 1:

"Much the <superlative>" is relatively uncommon, but nonetheless well attested.

Not many dictionaries seem to mention it explicitly; one that does is Macmillan Dictionary, which includes it in sense 2 ("used for emphasizing that someone or something is a lot bigger, better, worse etc"):

much the biggest/best etc (=a lot bigger, better etc than all the others): I got lots of lovely presents, but yours was much the nicest.

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Solution 2:

According to Michael Swan's Practical English Usage, this structure: much/quite + superlative noun phrase is mostly British. It is like by far+ superlative noun phrase. Quite in this structure means absolutely. For example: He is quite the most stupid man I've ever met.