Why do they put the word or title Master before a name in a letter or envelope?

Answer 1

It was the accepted way of addressing a young male in times gone by. A young woman would be Miss, a married one Mrs., an older man Esquire (after the name), plural would be Messrs.

Answer 2

The prefixes Dr., Mr, Mrs., Ms., Master or Messrs. before a name of some people or more than one person or a company, is just a polite way of addressing someone. It is a matter of etiquette to write another person's name with this prefix, though many people don't add the prefix in the US.