This idiom is most usually used to mean that a large number of people are anxious to discover or obtain something, and will come in droves. It also can mean that anyone who wants something badly enough will not let anything stop him or her from going to a particular place.
The earliest known usage is in the saying about building a better mousetrap, and is attributed to Ralph Waldo Emerson (1803-1882). Since at least the early 20th century, however, beating a path to someone’s door (or other locale) has been commonly used for numerous other things. The September 26, 1916 edition of Kentucky newspaper, The Mount Sterling Advocate, carries the following citation in ‘Merchants Try This,’ on page 6, column 1:
“Advertising will get the people to a store that is worth going to, but the merchant and his own goods must do the selling. Step up gentlemen. What merchant in this town wants the people to beat a path to his store?”