How authentic is the noble hadith: "A little evil for the sake of much good is much good," and what is its meaning?

The wording mentioned is not a Prophetic Hadith, nor has it been found in books of Sunnah or in compilations concerned with fabricated or weak Hadiths. It is most likely a jurisprudential and usuli (principles of Islamic law) قاعده (rule) stating that when faced with a conflict between two harms, one of which must be committed, the greater harm is avoided and the lesser harm is undertaken.