Very quickly and efficiently; very well. The simile is based on how houses made of timber or thatch burn very fast, as was the case with the log cabins of American pioneers. Washington Irving used the expression in Knickerbocker’s History of New York (1809), “At it they went like five hundred houses on fire,” and Dickens is quoted as having used it to mean very well (“I am getting on . . . like ‘a house on fire’”) in a letter of 1837.